Cohomology of uniserial $p$-adic space groups

p-adic Cohomology

The purpose of this paper is to survey some recent results in the theory of “p-adic cohomology”, by which we will mean several different (but related) things: the de Rham or p-adic étale cohomology of varieties over p-adic fields, or the rigid cohomology of varieties over fields of characteristic p > 0. Our goal is to update Illusie’s beautiful 1994 survey [I] by reporting on some of the many i...

p-adic Hurwitz groups

Herrlich showed that a Mumford curve of genus g > 1 over the p-adic complex field Cp has at most 48(g− 1), 24(g− 1), 30(g− 1) or 12(g− 1) automorphisms as p = 2, 3, 5 or p > 5. The Mumford curves attaining these bounds are uniformised by normal subgroups of finite index in certain p-adic triangle groups ∆p for p ≤ 5, or in a p-adic quadrangle group p for p > 5. The finite groups attaining these...

p-Adic deformations of arithmetic cohomology

THE SEGAL CONJECTURE FOR ELEMENTARY ABELIAN p-GROUPS-II. p-ADIC COMPLETION IN EQUIVARIANT COHOMOLOGY

This result implies an analogue for general finite groups, but we refer the reader to [25] and especially [S] for that. We shall give as efficient a proof of the theorem as present technology seems to allow, starting from the purely algebraic Ext calculation [4,1.1] of Adams, Gunawardena, and Miller as a given. When G=(Zp)‘, the theorem is due to those authors. However, their original passage f...

Behavior of $R$-groups for $p$-adic inner forms of quasi-split special unitary groups

‎We study $R$-groups for $p$-adic inner forms of quasi-split special unitary groups‎. ‎We prove Arthur's conjecture‎, ‎the isomorphism between the Knapp-Stein $R$-group and the Langlands-Arthur $R$-group‎, ‎for quasi-split special unitary groups and their inner forms‎. ‎Furthermore‎, ‎we investigate the invariance of the Knapp-Stein $R$-group within $L$-packets and between inner forms‎. ‎This w...