test_moissonnage_selune
type: Agent

The Newton stratification of Shimura varieties and the Arthur-Selberg trace formula
type: Dataset
contact point: Organization
  fn: CCSD
keyword: theorie-des-nombres
keyword: stratification-de-newton
keyword: theses
keyword: formule-des-traces
keyword: infoeu-reposemanticsdoctoralthesis
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: newton-stratification
keyword: varietes-de-shimura
keyword: number-theory
keyword: shimura-varieties
keyword: trace-formula
landing page: https://theses.hal.science/tel-00802976
description: We study the Newton stratification of Shimura varieties of PEL type, at the places of good reduction. We consider the basic stratum of certain simple Shimura varieties of PEL type at a place of good reduction. Under simplifying hypotheses we prove a relation between the l-adic cohomology of this basic stratum and the cohomology of the complex Shimura variety. In particular we obtain explicit formulas for the number of points in the basic stratum over finite fields, in terms of automorphic representations. We obtain our results using the trace formula and truncation of the formula of Kottwitz for the number of points on a Shimura variety over a finite field. We prove, using the trace formula that any Newton stratum of a Shimura variety of PEL-type of type (A) is non-empty at a prime of good reduction. This result is already established by Viehmann-Wedhorn; we give a new proof of this theorem. We consider the basic stratum of Shimura varieties associated to certain unitary groups in cases where this stratum is a finite variety. Then, we prove an equidistribution result for Hecke operators acting on the basic stratum. We relate the rate of convergence to the bounds from the Ramanujan conjecture of certain particular cuspidal automorphic representations on Gl_n. The Ramanujan conjecture turns out to be known for these automorphic representations, and therefore we obtain very sharp estimates on the rate of convergence. We prove that any connected reductive group G over a non-Archimedean local field has a cuspidal representation. Together with Erez Lapid we compute the Jacquet module of a Ladder representation at any standard parabolic subgroup of the general linear group over a non-Archimedean local field.
identifier: NNT: 2012PA112365
issued: 2026-05-12T05:59:43.773145
language: en
modified: 2026-05-12T05:59:43.773151

The Newton stratification of Shimura varieties and the Arthur-Selberg trace formula
type: Distribution
access URL: https://theses.hal.science/tel-00802976
format: HTML
issued: 2026-05-12T05:59:43.831101
modified: 2026-05-12T05:59:43.754982