Theodore SMITH, Plaintiff-Appellant v. Lieutenant Gabriel HEBERT; Warden Kevin Benjamin; Captain M. Laborde; Major C. Darbonne; Lieutenant Colonel Louis Stroud; Mental Health Worker Rachel Taylor; Captain Bo Whitaker; Lieutenant Chad Hukin; Lieutenant Todd Barrere; Lieutenant David Voorhies, Jr.; Burl Cain, Warden, Louisiana State Penitentiary; Richard Stalder, Secretary, Department of Public Safety and Corrections; Harold Sterling, Lieutenant Colonel; Unknown Stammriech, Captain (Camp J, C Team); Angela R. Day; Timothy Leonard; B. (Boris) Whitaker, Captain; James Tillman, Defendants-Appellees, 533 F. App'x 479

PER CURIAM: Plaintiff-Appellant Theodore Smith, Louisiana prisoner # 313084, fíled a civil rights complaint pursuant to 42 U.S.C. § 1983. According to Smith’s complaint, he filed a grievance against Warden Kevin Benjamin (ARP 1208) alleging that Benjamin violated Smith’s equal protection rights when he prevented Smith from being admitted to a vocational program because he is white. Smith alleges that when he refused to drop ARP 1208, the other defendants began retaliating against him by writing false disciplinary reports.

Those reports led to Smith’s filing ARP 1695 and ARP 2854 as well as several disciplinary appeals. The district court dismissed some of Smith’s claims pursuant to Rule 12(b)(6) of the Federal Rules of Civil Procedure, and it granted

summary judgment in favor of the defendants on the remainder of Smith’s claims. Smith now appeals. Equal Protection Claim Smith challenges the district court’s grant of

summary judgment to Warden Benjamin on Smith’s claim of an equal protection violation. We review a district court’s grant of

summary judgment de novo. Nickell v. Beau View of Biloxi, L.L.C., 636 F.3d 752, 754 (5th Cir.2011).

Summary judgment is appropriate when “the movant shows that there is no genuine dispute as to any material fact and the movant is entitled to judgment as a matter of law.” Fed.R.Civ.P. 56(a). To establish an equal protection violation, the plaintiff “must allege and prove that he received treatment different from that received by similarly situated individuals and that the unequal treatment stemmed from a discriminatory intent.” Taylor v. Johnson, 257 F.3d 470, 473 (5th Cir.2001).

The evidence shows that Smith applied for admission to a vocational program and that, despite any racial slurs that Benjamin might have made to Smith and regardless whether Benjamin had any authority to control admission to such programs, Smith was placed on the program’s waiting list. As no record evidence shows that Smith was intentionally treated differently from any similarly situated prisoner in this regard, the district court properly granted

summary judgment in favor of Benjamin. See Village of Willowbrook v. Olech, 528 U.S. 562, 564, 120 S.Ct. 1073, 145 L.Ed.2d 1060

(2000) Retaliation Claims The district court also determined that Defendants-Appellees Laborde and Taylor were entitled to judgment as a matter of law on Smith’s claims of retaliation. “To prevail on a claim of retaliation, a prisoner must establish (1) a specific constitutional right, (2) the defendant’s intent to retaliate against the prisoner for his or her exercise of that right, (3) a retaliatory adverse act, and (4) causation.” Morris v.

Powell, 449 F.3d 682, 684 (5th Cir.2006) (internal quotation marks and citation omitted). “The inmate must produce direct evidence of motivation or, the more probable scenario, allege a chronology of events from which retaliation may plausibly be inferred.” Woods v. Smith, 60 F.3d 1161, 1166 (5th Cir.1995) (internal quotation marks and citation omitted). Smith alleged that on June 5, 2007, La-borde wrote a false disciplinary report charging Smith with having sold drugs to another inmate.

In connection with this same event, Smith alleged that Gabriel Hebert, who was responsible for investigating the charge, submitted fabricated information from confidential informants. He also alleged that Louis Stroud sentenced him to a quarters change from the Hickory Unit to Camp D despite the fact that the drug-trafficking charge was dismissed. Smith claimed that all of these actions were taken in retaliation for his refusal to drop his grievances against Benjamin.

On appeal, Smith contends that the district court improperly decided a factual dispute as to whether Laborde had an intent to retaliate against Smith when he wrote the disciplinary report. The district court, however, did not make such a determination; rather it concluded that because the charge had been dismissed and no penalty had been imposed, Smith had not shown any injury resulting from Laborde’s actions. Smith nevertheless persists that there was a sentence imposed.

Even if there is a genuine dispute on this point, that fact is not material. “Retaliation against a prisoner is actionable only if it is capable of deterring a person of ordinary firmness from further exercising his constitutional rights.” Morris, 449 F.3d at 686. A transfer to a more dangerous prison as a penalty for the exercise of constitutional rights has the potential to be such a deterrent. Id. at 687. Smith asserts on appeal that Camp D is a more violent camp than the main prison; however, nothing in the

summary judgment evidence establishes that Camp D is in any way more violent than the main prison. Absent such a showing, there is no indication that the transfer in question was actionable even if we assume that it was motivated by an intent to retaliate. See id. at 686. Accordingly, the court properly granted

summary judgment to Laborde. As Smith maintains, however, the district court did err in finding that his retaliation claim against Stroud was unex-hausted. Additionally, in light of the record, the district court erred in construing Smith’s retaliation claim against Hebert as only an unfair-investigation claim and dismissing that claim pursuant to Rule 12(b)(6). Because there is no evidence that the transfer to Camp D was sufficiently injurious to be actionable, however, Stroud and Hebert were entitled to

summary judgment dismissing Smith’s retaliation claims against them. We therefore affirm the district court’s judgment with respect to these two defendants on this alternative ground. See Disraeli v. Rotunda, 489 F.3d 628, 635 (5th Cir.2007). Smith alleged that Taylor retaliated against him for filing ARP 1208 against Benjamin when, on July 6, 2007, she filed a disciplinary report stating that Smith walked into her office without knocking, handed her a letter that contained sexual content and contact information, and told her not to tell anyone about the letter. The district court granted

summary judgment on this claim, finding no evidence that Taylor knew about ARP 1208 at the time she wrote the report. To show the causation necessary to succeed on a retaliation claim, a prisoner must show that the adverse act would not have occurred but for the retaliatory motive. McDonald v. Steward, 132 F.3d 225, 231 (5th Cir.1998). Taylor charged Smith, inter alia, under Rule 30 of the prison’s disciplinary rules, which describes generally prohibited behavior.

As the disciplinary report was also based on the fact that Smith walked into Taylor’s office without knocking, we agree with the district court’s determination that Smith did not show the requisite but-for causation with respect to his retaliation claim against Taylor. The district court granted

summary-judgment to Defendants-Appellees Hukin and Whitaker on Smith’s claims of retaliation and use of excessive force on the ground that Smith had failed to exhaust his administrative remedies on those claims. It likewise granted

summary judgment on exhaustion grounds on Smith’s claims of retaliation against Todd Barrere, David Voorhies, Harold Sterling, and Tillman. Our de novo review of the competent

summary judgment evidence satisfies us that the district court ruled correctly that these claims were unex-hausted. As Smith alleged that Benjamin and Chad Darbonne had threatened him with retaliation but did not allege that they had committed any specific retaliatory adverse acts against him, those retaliation claims were properly dismissed pursuant to Rule 12(b)(6). See Ashcroft v. Iqbal, 556 U.S. 662, 678, 129 S.Ct. 1937, 173 L.Ed.2d 868 (2009); Morris, 449 F.3d at 684.

The district court also construed as evidence of retaliation Smith’s allegations against Benjamin and Darbonne as an independent claim of verbal abuse. Finding that such verbal abuse did not rise to the level of a constitutional violation, the district court dismissed the claim pursuant to Rule 12(b)(6). Smith does not challenge this assessment of his verbal-abuse claim, and he has abandoned the issue on appeal. See Yohey v. Collins, 985 F.2d 222, 224-25 (5th Cir.1993); Brinkmann v. Dallas County Deputy Sheriff Abner, 813 F.2d 744, 748 (5th Cir.1987).

Other Issues Without providing any citation to the record, Smith asserts that the magistrate judge erred when she denied him leave to amend his complaint to add retaliation and civil conspiracy claims against Todd Barrere, David Voorhies, Captain Stammreich, and James Tillman. Smith filed numerous motions to amend and supplement his complaint, with mixed results. The unsuccessful motion that comes closest to being that described by Smith in his appellate brief is one in which Smith sought to add new claims against Tillman. Unlike motions to amend, motions to supplement need not be freely granted. See Burns v.

Exxon Corp., 158 F.3d 336, 343 (5th Cir.1998). Denying Smith’s motion was not an abuse of discretion because the proposed supplemental claims against Tillman were not related to the original cause of action, and the inclusion of those claims would have unduly complicated and prolonged an already complicated case. See id,.; Lewis v. Knutson, 699 F.2d 230, 239 (5th Cir.1983). Smith also challenges a pretrial order that he maintains was confusing and caused him to label his objection to the defendants’ motion for

summary judgment as also being a cross-motion for

summary judgment. Although this court liberally construes pro se briefs, even pro se litigants must brief arguments to preserve them. Yohey, 985 F.2d at 225. Smith does not provide a record citation for the order he challenges; neither does he cite any law or standard of review that would be applicable to such a challenge. By failing to brief this issue adequately, Smith has effectively abandoned it. See id. at 224-25.

Referencing the time he spent in administrative segregation and in Camp J, an extended lockdown camp, Smith challenges the district court’s ruling that he did not allege that he had suffered any actual injury. “No Federal civil action may be brought by a prisoner confined in a jail, prison, or other correction facility, for mental or emotional injury while in custody without a prior showing of physical injury.” 42 U.S.C. § 1997e(e).

As Smith did not allege any physical injury stemming from his confinement in administrative segregation or in Camp J, the district court did not err in dismissing Smith’s claims that he was confined to a cell with inadequate sunlight and fresh air pursuant to Rule 12(b)(6). Smith maintains that he stated a valid claim that all of the defendants had conspired to retaliate against him. A conspiracy claim requires showings that an actual violation of § 1983 occurred and that the defendants agreed to commit an illegal act. See Hale v. Townley, 45 F.3d 914, 920 (5th Cir.1995); Arsenaux v.

Roberts, 726 F.2d 1022, 1024 (5th Cir.1982). As no § 1983 violation was established, Smith’s claim of civil conspiracy was properly dismissed under Rule 12(b)(6). See Hale, 45 F.3d at 920. Finally, the district court determined that Smith’s claim relating to the filing of a July 2006 disciplinary report was prescribed and that his claim that Voorhies and Barrere destroyed his property in December 2007 failed because Smith had an adequate state remedy for that claim. Smith has abandoned any appeal of these issues by failing to challenge them in this court. See Yohey, 985 F.2d at 225; Brinkmann, 813 F.2d at 748.

The judgment of the district court is, in all respects, AFFIRMED. Pursuant to 5th Cir. R. 47.5, the court has determined that this opinion should not be published and is not precedent except under the limited circumstances set forth in 5th Cir. R. 47.5.4.