Hodge-Newton filtrations, cell decomposition and cohomology of certain p-adic moduli spaces
type: Dataset
description: In this thesis we study p-adic analytic geometry and l-adic cohomology of some Rapoport-Zink spaces, using the theory of Harder-Narasimhan filtration of finite flat group schemes developed by Fargues .This thesis consists of three parts. The first part deals with some non-basic Rapoport-Zink spaces, which satisfy the condition that their Newton polygon and Hodge polygon have a non-trivial contact point, which is a breakpoint for the Newton polygon. Under this hypothesis, we prove these Rapoport-Zink spaces can be decomposed as a direct sum of smaller Rapoport-Zink spaces associated to some suitable parabolic subgroups, thus their l-adic cohomology is parabolically induced and in particular contain no supercuspidal representations. We prove these facts by first proving a theorem about the Hodge-Newton filtration for p-divisible groups with additional structures over complete valuation rings of rank one and mixed characteristic (0,p).In the second part, we consider the basic Rapoport-Zink spaces with signature (1,n-1) for the unitary groups associated to the unramified quadratic extension of Qp. We study the Hecke action on these spaces in details. By using the theory of Harder-Narasimhan filtrations of finite flat group schemes, and the Bruhat-Tits stratification of the reduced special fiber Mred studied by Vollaard-Wedhorn, we find some compact analytic domain DK such that its translates under the group G(Qp)×Jb(Qp) form a locally finite cover of the whole space MK. We call such a phenomenon a locally finite cell decomposition.In the third part we prove a Lefschetz trace formula for these spaces for the action of regular semi-simple elliptic elements, by considering the action of these elements on the cells and applying Mieda's main theorem. In the same way we can also reprove the Lefschetz trace formula for Lubin-Tate spaces as previously obtained by Strauch and by Mieda. This Lefschetz trace formula should characterize the realization of local Jacquet-Langlands co…
identifier: NNT: 2012PA112341
issued: 2026-05-31T15:14:12.869822
language: en
modified: 2026-05-31T15:14:12.869827
contact point: Organization
  fn: CCSD
keyword: cell-decomposition
keyword: decomposition-cellulaire
keyword: espaces-de-rapoport-zink
keyword: filtration-de-hodge-newton
keyword: formule-de-lefschetz
keyword: groupes-p-divisibles
keyword: hodge-newton-filtration
keyword: infoeu-reposemanticsdoctoralthesis
keyword: lefschetz-trace-formula
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: p-divisible-groups
keyword: rapoport-zink-spaces
keyword: theses
landing page: https://theses.hal.science/tel-00764117

Hodge-Newton filtrations, cell decomposition and cohomology of certain p-adic moduli spaces
type: Distribution
format: HTML
issued: 2026-05-31T15:14:13.036822
modified: 2026-05-31T15:14:12.832454
access URL: https://theses.hal.science/tel-00764117

test_moissonnage_selune
type: Agent