Page:United States Reports, Volume 542.djvu/505

466

No. 03–334.

(a) The District Court has jurisdiction to hear petitioners' habeas challenges under 28 U.S.C. § 2241, which authorizes district courts, "within their respective jurisdictions," to entertain habeas applications by persons claiming to be held "in custody in violation of the laws  of the United States," §§ 2241(a), (c)(3). Such jurisdiction extends to aliens held in a territory over which the United States exercises plenary and exclusive jurisdiction, but not "ultimate sovereignty." Pp. 473–484.

(1) The Court rejects respondents' primary submission that these cases are controlled by Eisentrager ' s holding that a District Court