José Luis DÍAZ-COLÓN, on his own behalf and on behalf of his minor son J.L.D.R.; Linda Delgado, on behalf of her minor daughter D.M.D.D.; Zoraida Colón-Cartagena; Pedro Diaz; Pedro Luis Díaz-Colón; Yahaira Enid Díaz-Colón; Lourdes De Jesús-Velázquez, on her own and on behalf of her minor children J.L.S.D.; J.L.L.S.D., on their own and as legal heirs of Leopoldo Sanabria-Diaz; L.S.D., on their own and as legal heirs of Leopoldo Sanabria-Diaz; Albaela Diaz-Caraballo; Leonardo Sanabria-Diaz; Jennifer Piris-Jusino, on her own and on behalf of her minor daughter G.R.P.; Lucy Guzmán-Borrero; Carmelo Velázquez-Colón; Carmelo Colón-Rivera; Orlando Colón-Velázquez; Orlando Ramos-Félix; Josefa Félix; José Antonio Félix; Elíseo Ramos-Félix; Juan Marcos Merced-Gómez; Héctor Merced-Rodríguez; María E. Gómez-Velázquez; Leopoldo Sanabria-Morales; Maribel Ortiz-Vázquez, on behalf of minor, J.M.S.O; Ana Luisa Diaz-Rivera; Yolanda Ortiz-Díaz; Evelyn Ortiz-Díaz; Luis Daniel Ortiz-Díaz; Digno OrtizDíaz; Francis I. López-Díaz; Chelsea Luz Merced; Héctor Julio Merced-Gómez, Plaintiffs, Appellees, v. José A. FUENTES-AGOSTINI; Gabriel Redondo; Juan José Toledo-Bayouth; José Capó; José Toledo-Bayouth; Fernando Toledo-Bayouth; Pedro J. Toledo-Bayouth; Aníbal Solivan-Solivan; Héctor Tirado; Daniel Colón; Francisco Báez-Quiñones; Jesús Figueroa-Cruz, Defendants, Appellants, Pedro Toledo-Dávila; FNU Candelaria; Estate of Ulpiano-Crespo, comprised of unknown individuals K through S; José Figueroa; Ulpiano Crespo; Zoé Díaz-Colón; Conjugal Partnership Báez-Doe; Conjugal Partnership Capó-Doe; Conjugal Partnership Colon-Doe; Conjugal Partnership Diaz-Doe; Conjugal Partnership Figueroa-Doe; Conjugal Partnership Fuentes-Doe; Conjugal Partnership RedondoDoe; Conjugal Partnership SolivanDoe; Conjugal Partnership TiradoDoe; Conjugal Partnership Toledo-Doe, Defendants, 786 F.3d 144

KAYATTA, Circuit Judge. This lawsuit arises 'out of two sets of wrongful murder convictions in Puerto Rico’s courts. In each murder trial, jurors convicted a group of individuals based in large part on the testimony of a single witness, Zoé Díaz-Colón (“Díaz”). After one of the convicted individuals killed himself in prison, Diaz came forward to recant her testimony, claiming that law enforcement personnel had coerced and bribed her into giving fabricated testimony.

After the Commonwealth courts subsequently vacated the convictions, and all charges against them were dropped, the wrongfully convicted individuals (and/or their heirs and family members) filed these consolidated civil damages actions in federal court against police officers and prosecutors involved in their misbegotten prosecutions. Nine of those law enforcement defendants (or their heirs) now appeal from the denial of their respective motions for

summary judgment based on absolute or qualified immunities. We reverse in part the denial of

summary judgment for assistant district attorney Gabriel Redondo-Miranda (“ADA Redondo”), but otherwise affirm the district court’s rulings. I. Background Because this appeal arises from the denial of the defendants’ motions for

summary judgment, we present the facts in the light most favorable to the plaintiffs, accepting as true all of the inferences the district court drew in the plaintiffs’ favor. Cady v. Walsh, 753 F.3d 348, 350 (1st Cir.2014). And because our review in this case is interlocutory, we train our focus on rulings of law, rather than assessments of fact. Id. at 358-59. A. Factual Background , Puerto Rico police hired Díaz as a paid informant on August 2, 1995. The following day, Rafael Colomba was murdered in Salinas, Puerto Rico. More than two years later Antonio Peña was murdered in Salinas on November 5, 1997.

Defendant police agent Jesús Figueroa-Cruz (“Agent Figueroa”) investigated the Colomba murder, and defendant police agent Francisco Báez-Quiñones (“Agent Báez”) led the investigation into Peña’s murder.

The investigations stalled until June of 1998, when Diaz gave two sworn statements at the Guayama police station claiming both that: (1) she heard Orlando Ramos-Félix, Carmelo Vélazquez Colón, and Leopoldo Sanabria-Díaz (“Sanabria”) plan and later admit to the Colomba murder; and (2) she also heard José Díaz-Colón, Héctor Merced Gómez, and Manuel Ortiz (“Ortiz”) plan and later admit to the Peña murder. .Agent Figueroa and defendant assistant district attorney José Capó (“ADA Capó”) were present for the taking of Diaz’s statement on the Colomba murder.

ADA Re-dondo did not participate in the investigation of either murder. Diaz was the key prosecution witness at both murder trials. No one told defense counsel during either trial that Diaz had been a paid confidential informant for the police. Based on Diaz’s testimony in the respective trials, both sets of plaintiffs were convicted and sentenced to prison. Ortiz committed suicide soon after his conviction for the Peña murder in May of 1999. After learning in 2001 of Ortiz’s suicide, Diaz recanted, claiming in a sworn declaration that her trial testimony against the plaintiffs was fabricated.

Diaz’s recantation led to motions from the four living convicts for new criminal trials. At the hearings on those motions, Diaz testified that Agent Báez knew that she was a paid informant, and that he coerced, bribed, and coached her into giving the statements implicating plaintiffs in the Colomba or Peña murders. Diaz testified that Agent Báez told her what to say, familiarized her with the murder scenes and photographs of the plaintiffs, and repeatedly met with her to rehearse her statements, which she memorized. She claimed, too, that Agent Figueroa attended some of these rehearsals.

Diaz further testified that Agent Báez and a prosecutor offered her housing and custody of her children in exchange for testimony consistent with her sworn statements. In addition, she testified that ADA Redon-do offered her a therapy machine for her asthma while she was staying in a witness protection shelter during one of the trials in which she testified falsely for the prosecution.

In 2008, the Supreme Court of Puerto Rico vacated plaintiff Velázquez’s conviction and granted a new trial on the ground that the prosecutors had not timely disclosed exculpatory evidence, including Diaz’s contract as a paid informant. Pueblo v. Velázquez-Colón, 174 D.P.R. 304 (2008). Shortly thereafter, the government requested and the trial court ordered the dismissal of the criminal charges against all of the plaintiffs. B. Procedural Background The plaintiffs associated with each group of wrongfully convicted individuals commenced separate actions in federal court against the same set of defendants.

The district court consolidated the two cases. The plaintiffs asserted claims under 42 U.S.C. § 1983 for violations of the Fourth and Fourteenth Amendments, and various constitutional and tort claims under Puerto Rico law. After the district court granted in part defendants’ motion to dismiss some of the claims, only Agent Báez, Agent Figueroa, and ADA Redondo remained as targets of the federal

section 1983 claims (for malicious prosecution under the Fourth Amendment and conspiracy to deprive plaintiffs of their rights under federal law). Diaz-Colon v. Toledo-Davila, 922 F.Supp.2d 189, 209-10 (D.P.R.2013). State tort and vicarious liability claims under Puerto Rico law remained against all of the defendants who are parties to this appeal. Id. During discovery, plaintiffs scheduled Diaz’s deposition in Puerto Rico. But Diaz fled Puerto Rico shortly before her deposition because she allegedly received threats at her hotel. Subsequent attempts to

schedule her deposition by video failed. ■ After the close of discovery, defendants moved for

summary judgment on a variety of grounds, including that they were entitled to qualified or absolute immunity and that there was insufficient evidence to support plaintiffs’ claims. To oppose defendants’ motion for

summary judgment, plaintiffs relied heavily on the transcripts of Diaz’s 2001 testimony during the hearings on the motions for new criminal trials. Plaintiffs also filed a motion in limine seeking a ruling on the admissibility of the transcripts of Diaz’s 2001 testimony under the hearsay exceptions applicable to former testimony, to statements against interest, and to otherwise reliable out-of-court communications. See Fed.R.Evid. 804(b)(1), (3); 807.

That testimony described outright fraud by some of the defendants — but not ADA Redondo — in fabricating evidence that was then used to secure an indictment and subsequent prosecution. It also supported a finding that ADA Redondo offered Diaz an asthma machine while she was staying in the witness protection shelter during a trial. In their reply to plaintiffs’ opposition to

summary judgment and in their opposition to plaintiffs’ motion in limine, defendants contested the admissibility of the transcripts. Rather than addressing the merits of defendants’ qualified immunity defense, the district court rejected the defense on procedural grounds as insufficiently argued and briefed.

In so ruling, the district court observed that defendants “d[id] not specify ... which individuals are purportedly protected by qualified immunity or for what conduct,” and instead “merely cite[d] federal case law regarding qualified immunity, without applying it to the facts of their case.” As for ADA Redondo’s absolute immunity defense, the district court rejected it on the merits, concluding somewhat cryptically that the evidence would support a finding that ADA Redondo offered Diaz an asthma machine in exchange for her testimony.

Finally, on the state law claims, the court “note[d] its frustration with the poorly pled arguments made by all parties” and refused to consider those arguments as well. The district court also found that defendants’ exclusive reliance on federal qualified immunity case law precluded the court from determining whether any of the defendants were entitled to immunity from the Puerto Rico law claims. This interlocutory appeal followed. II. Analysis A.

The Qualified Immunity Defenses In their main brief on appeal, defendants present over fifty pages of con-clusory assertions, discursive digressions, and factual contentions largely bereft of record citations or salient organization, all under the rubric of a single argument: “The district court erred in denying

summary judgment as to the issues of qualified and/or absolute immunity, inasmuch as the court centered its ruling on inadmissible hearsay evidence.” The hearsay to which defendants refer are the transcripts of Diaz’s testimony in which she recanted her prior trial testimony and described what plaintiffs point to as the coercion, bribes, and coaching that produced her false testimony leading to and presented in the criminal trials. The problem for all appellants other than ADA Redondo is that the district court plainly did not center its qualified immunity ruling on any evidence at all, admissible or not. Rather, it denied their request for

summary judgment to the extent that their request was based on qualified immunity defenses under state and federal law for an entirely independent, procedural reason: defendants’ failure to explain how the law applied to the facts concerning each defendant. Piling one omission on top of another, defendants fail to develop any argument in their brief on appeal for why the district court erred in finding defendants’ confusing and poorly structured motion papers insufficient even to bring forward their 'defenses.

Indeed, defendants’ .lengthy brief to us makes no mention of the district court’s actual grounds- for its ruling on the qualified immunity defenses. And even after plaintiffs’ opposing brief drew this defalcation to defendants’ attention, the reply brief offers no reference to any argument or analysis that belies the district court’s conclusion. Instead, defendants merely assert that there was evidence in the record that the district court ignored, which misses the point. We share the district court’s frustration with the inadequate briefing submitted on behalf of the defendants.

It is black letter law that “we deem waived claims not made or claims adverted to in a cursory fashion, unaccompanied by developed argument.” Rodríguez v. Municipality of San Juan, 659 F.3d 168, 175 (1st Cir.2011); cf. De Araujo v. Gonzales, 457 F.3d 146, 152-53 (1st Cir.2006) (petitioner’s failure to challenge Board of Immigration Appeal’s

summary dismissal of his case for failure to file a brief waived his argument on the merits). For this simple reason, we reject the appeal of all defendants to the extent it is predicated on their qualified immunity defenses under federal or state law. B. ADÁ Redondo’s Absolute Immunity Defense That leaves only ADA Redondo’s appeal of the denial of his absolute immunity defense to the federal claims against him. He argues that the district court erred in denying his motion for

summary judgment based on his absolute immunity-defense. The district court rejected that defense on the merits, based solely on the finding that “[e]vidence in the record suggests that [ADA Redondo] offered Diaz-Colon an asthma therapy machine in exchange for her testimony.” ADA Redondo’s initial argument for reversing the district court’s finding against him is that the 2001 testimony of Diaz upon which the court relied will not be admissible at trial, see Fed.R.Civ.P. 56(c)(2), because Diaz will not appear to testify.

This argument seems to be quite a stretch given that Diaz’s sworn 2001 testimony confessing to and describing her elaborate perjury had a great “tendency ... to expose [Diaz] to civil or criminal liability,” and was thus most likely admissible as an exception to the rule against hearsay. Fed.R.Evid. 804(b)(3)(A); see also United States v. Jiménez, 419 F.3d 34, 43 (1st Cir.2005); Whitlock v. Brueggemann, 682 F.3d 567, 575 (7th Cir.2012). Additionally, even if the argument had some hope of success, it is not clear that we could consider it given the interlocutory nature of this appeal.

Compare Whitlock, 682 F.3d at 575 (no review of evidentiary issue on interlocutory appeal); and Ellis v. Washington Cnty., 198 F.3d 225, 229 (6th Cir.1999) (same); with Mersch v. City of Dallas, 207 F.3d 732, 735 (5th Cir.2000) (reviewing evidentiary issue). Ultimately, we need not rule on this evidentiary argument or examine more closely our jurisdiction even to consider such an argument on interlocutory review. Rather, we turn to and rely on a second argument that Redondo advances for reversing the

summary judgment denial on its merits. That argument challenges the district court’s conclusion that, if ADA Redondo did what Diaz says he did (offer her an asthma therapy machine in exchange for her testimony), his immunity as a prosecutor would not protect him. The basic principles applicable to assertions of absolute prosecutorial immunity are set forth in Van de Kamp v. Goldstein, 555 U.S. 335, 129 S.Ct. 855, 172 L.Ed.2d 706 (2009). See also Knowlton v. Shaw, 704 F.3d 1, 5 (1st Cir.2013).

Prosecutorial immunity applies to conduct “ ‘intimately associated with the judicial phase of the criminal process.’ ” Van de Kamp, 555 U.S. at 343, 129 S.Ct. 855 (quoting Imbler v. Pachtman, 424 U.S. 409, 430, 96 S.Ct. 984, 47 L.Ed.2d 128 (1976)). Deciding where to draw the line between such immunized prosecutorial advocacy and conduct that is, for example, exclusively' investigative or administrative is not always easy. See, e.g., Genzler v. Longanbach, 410 F.3d 630, 637 (9th Cir.2005) (“[T]he Supreme Court has resisted any attempt to draw a bright-line between” advocacy and investigation).

Nevertheless, our task in this case is made somewhat easier by the district court’s uncontested finding that ADA Redondo did not participate in, or advise the police in connection with, the investigations of the murders. This finding rules out the possibility that ADA Redondo had anything to do with inducing Diaz to give the false statements that implicated plaintiffs in the unsolved crimes. Cf. Buckley v. Fitzsimmons, 509 U.S. 259, 274, 113 S.Ct. 2606, 125 L.Ed.2d 209 (1993) (no immunity for fabricating evidence before probable cause established); Burns v.

Reed, 500 U.S. 478, 496, 111 S.Ct. 1934, 114 L.Ed.2d 547 (1991) (no immunity for giving advice to police during investigation). Instead, his involve-merit was limited to his actions as a prosecutor in connection with preparing the Commonwealth’s evidence at trial. And it has long been clear that absolute immunity bars a damages action against a prosecutor for presenting testimony at trial even if the prosecutor knows that the testimony is false. Imbler, 424 U.S. at 430-31 & n. 33, 96 S.Ct. 984.

The assertion in this case that the prosecutor not only presented false testimony, but also offered something of value to induce a trial witness to testify creates no basis for concluding that the conduct was any less “intimately associated with the judicial phase of the criminal proceeding.” Id. at 430, 96 S.Ct. 984. Preparing trial witnesses is at the core of what a prosecutor qua prosecutor does, and the trial itself is the quintessential judicial proceeding.

Buckley, 509 U.S. at 273, 113 S.Ct. 2606 (immune tasks “include the professional evaluation of the evidence assembled by the police and appropriate preparation for its presentation at trial”). Prosecutors regularly prepare and present testimony by witnesses to whom the government has offered inducements to secure their cooperation. Disclosure requirements and due process principles provide some protection to criminal defendants from abuses of this practice. Brady v. Maryland, 373 U.S. 83, 87, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963); Napue v.

Illinois, 360 U.S. 264, 269, 79 S.Ct. 1173, 3 L.Ed.2d 1217 (1959) (“[I]t is established that a conviction obtained through use of false evidence, known to be such by representatives of the State, must fall under the Fourteenth Amendment.”) (citing Mooney v. Holohan, 294 U.S. 103, 112-13, 55 S.Ct. 340, 79 L.Ed. 791 (1935) (per curiam)). It is another thing altogether, .though, to provide wrongfully charged individuals with a private damages remedy against prosecutors when cooperating witnesses lie.

If prosecutors could be sued civilly every time any such witness claimed a wrongful inducement to lie, prosecutors might well be exposed to numerous such suits. Weighing the costs and benefits to the public interest of such an exposure to civil liability, the law bars such claims when they arise out of the prosecutor’s work in a criminal proceeding. See Dory v. Ryan, 25 F.3d 81, 83 (2d Cir.1994); Rose v. Bartle, 871 F.2d 331, 344-45 (3d Cir.1989). See generally, Van de Kamp, 555 U.S. at 342, 129 S.Ct. 855 (discussing policy reasons for shielding prosecutors).

In a last-ditch effort, plaintiffs’ counsel argued that ADA Redondo’s participation on “the prosecution team” defeated absolute immunity, presumably by making him liable for the misconduct of others in the previous procuring of the false statements.

Adopting this approach would render prosecutors vicariously liable in all cases involving improper actions since, at some point, a prosecutor is always a member of “the prosecution team.” Such an exponential increase in potential liability plainly conflicts with the purpose of affording prosecutors absolute immunity, to insulate prosecutorial discretion and resources from the threat of litigation. Van de Kamp, 555 U.S. at 345, 129 S.Ct. 855; Imbler, 424 U.S. at 424-25, 96 S.Ct. 984. Absolute immunity therefore shields ADA Redondo from having to stand trial for the malicious prosecution and conspiracy claims under

section 1983. III. Conclusion We reverse and remand for entry of

summary judgment for ADA Redondo on plaintiffs’ federal claims for malicious prosecution and conspiracy. We otherwise affirm the district court’s denial of

summary judgment, and remand for proceedings consistent with this decision. . Jesús Figueroa-Cruz and Jesús Figueroa-de Jesús are listed as separate defendants on the docket, but they are in fact the same person. In his answer to the amended complaint, Agent Figueroa clarified that his correct name is Jesús Figueroa-Cruz. . Diaz also testified for prosecutors in yet a third murder trial against a criminal defendant who is not a plaintiff in this case. . In 2003, after the Puerto Rico trial court denied his motion for a new trial, Sanabria also committed suicide in prison. .

We deny as moot plaintiffs' motion, opposed by defendants, to file with this court a supplemental appendix containing the excerpts of Diaz’s transcribed testimony that plaintiffs relied on in the district court to oppose

summary judgment. See Fed. R.App. P. 30(a)(2) ("Parts of the record may be relied on by the court or the parties even though not included in the appendix."). . That prosecutor has since died. The plaintiffs sued his estate, but.his heirs did not appear and are not appellants. . The parties submitted to the district court a certified English translation of the Supreme Court of Puerto Rico opinion. ECF No. 300-1. . The plaintiffs also sued Diaz, who did not answer or appear. The district court entered a default against her in the first case, no. 09-1835, before the two cases were consolidated. .

The defendants-appellants who face only state law claims are former Secretary of Justice José Fuentes-Agostini (Puerto Rico’s equivalent of a state attorney general), ADA Capó, police captains Aníbal Solivan-Solivan and Héctor Tirado, police sergeant Daniel Colón, and members of the estate of former Puerto Rico Police Superintendent Pedro Toledo-Dávila. . The evidence strongly suggests that ADA Redondo made this offer when Diaz experienced medical difficulties during yet a third, later trial at which Diaz testified, and that he disclosed the offer to defense counsel and to the court.

The criminal defendant in that later trial was acquitted and is not a plaintiff in this case. But, in view of the

summary judgment standards, we will assume that the offer occurred in one of the two trials in which some of the plaintiffs were convicted. .After filing their notice of appeal, defendants sought from this court a stay qf trial pending the appeal. Another panel of this court granted the stay with the instruction that the parties brief “the appealability of the issue of the admissibility of evidence on which the district court relied in denying

summary judgment on the ground of qualified immunity,” and directed the parties to Mersch v. City of Dallas, 207 F.3d 732, 735 (5th Cir.2000), as a starting point. . This holding does not mean that all of the remaining claims against all of these defendants will ultimately make it to the factfinder. See Fed.R.Civ.P. 50(a); Camilo-Robles v. Hoyos, 151 F.3d 1, 9 (1st Cir.1998) ("When a defendant fails on a pretrial qualified immunity claim, he nonetheless can plead qualified immunity as an affirmative defense and resurrect the claim at trial.”). Rather, we hqld only that these defendants both below and on appeal have waived any ability to secure

summary judgment in their favor. . We do note that the undifferentiated structure of defendants’ appellate briefing, the jumbling together of all the defendants, and the lack' of any helpful table of contents or argument headings came close to causing us to consider this argument waived as well.