Shimura varieties at level and Galois representations
Artikel i vetenskaplig tidskrift, 2020

We show that the compactly supported cohomology of certain - or -Shimura varieties with -level vanishes above the middle degree. The only assumption is that we work over a CM field in which the prime splits completely. We also give an application to Galois representations for torsion in the cohomology of the locally symmetric spaces for. More precisely, we use the vanishing result for Shimura varieties to eliminate the nilpotent ideal in the construction of these Galois representations. This strengthens recent results of Scholze [On torsion in the cohomology of locally symmetric varieties, Ann. of Math. (2) 182 (2015), 945-1066; MR 3418533] and Newton-Thorne [Torsion Galois representations over CM fields and Hecke algebras in the derived category, Forum Math. Sigma 4 (2016), e21; MR 3528275].

11F80

14G22

2010 Mathematics Subject Classification

11F75

11G18

Författare

Ana Caraiani

Imperial College London

Daniel R. Gulotta

Columbia University

Chi Yun Hsu

Harvard University

Christian Johansson

Chalmers, Matematiska vetenskaper, Algebra och geometri

Lucia Mocz

Universität Bonn

Emanuel Reinecke

University of Michigan

Sheng Chi Shih

Laboratoire Paul Painlevé

Compositio Mathematica

0010-437X (ISSN) 1570-5846 (eISSN)

Vol. In Press

Ämneskategorier

Algebra och logik

Geometri

Matematisk analys

DOI

10.1112/S0010437X20007149

Mer information

Senast uppdaterat

2020-07-01