Representations of p-adic groups over commutative rings

MF Vignéras - Prize LectureS, 2022 - ems.press
Motivated by the Langlands program in representation theory, number theory, and geometry,
the theory of representations of a reductive p-adic group, originally in complex vector …

Supercuspidal representations of GLn (F) distinguished by a Galois involution

V Sécherre - Algebra & Number Theory, 2019 - msp.org
Abstract Let F∕ F 0 be a quadratic extension of nonarchimedean locally compact fields of
residual characteristic p≠ 2 and let σ denote its nontrivial automorphism. Let R be an …

Repr\'esentations cuspidales de GL (r, D) distingu\'ees par une involution int\'erieure

V Sécherre - arXiv preprint arXiv:2005.05615, 2020 - arxiv.org
Let n be a positive integer, F be a non-Archimedean locally compact field of odd residue
characteristic p and G be an inner form of GL (2n, F). This is a group of the form GL (r, D) for …

Towards an explicit local Jacquet–Langlands correspondence beyond the cuspidal case

V Sécherre, S Stevens - Compositio Mathematica, 2019 - cambridge.org
Towards an explicit local Jacquet–Langlands correspondence beyond the cuspidal case
Page 1 Towards an explicit local Jacquet–Langlands correspondence beyond the cuspidal …

Representations of -adic groups over coefficient rings

MF Vignéras - arXiv preprint arXiv:2205.02019, 2022 - arxiv.org
Motivated by the Langlands program in representation theory, number theory and geometry,
the theory of representations of a reductive $ p $-adic group over a coefficient ring different …

Cuspidal -modular representations of distinguished by a Galois involution

R Kurinczuk, N Matringe, V Sécherre - arXiv preprint arXiv:2310.15820, 2023 - arxiv.org
Let $ F/F_0 $ be a quadratic extension of non-Archimedean locally compact fields of
residual characteristic $ p\neq2 $ with Galois automorphism $\sigma $, and let $ R $ be an …

The inertial Jacquet-Langlands correspondence

A Dotto - arXiv preprint arXiv:1707.00635, 2017 - arxiv.org
We give a parametrization of the simple Bernstein components of inner forms of a general
linear group over a local field by invariants constructed from type theory, and explicitly …

Supercuspidal representations of GLn (F) distinguished by a unitary involution

J Zou - Bull. Soc. Math. France, 2022 - smf.emath.fr
Let F/F0 be a quadratic extension of non-Archimedean locally compact fields of residue
characteristic p= 2. Let R be an algebraically closed field of characteristic different from p …

An analogue of ladder representations for classical groups

H Atobe - International Mathematics Research Notices, 2024 - academic.oup.com
In this paper, we introduce a notion of ladder representations for split odd special orthogonal
groups and symplectic groups over a non-archimedean local field of characteristic zero. This …

Breuil-M\'ezard conjectures for central division algebras

A Dotto - arXiv preprint arXiv:1808.06851, 2018 - arxiv.org
We formulate an analogue of the Breuil-M\'ezard conjecture for the group of units of a central
division algebra over a $ p $-adic local field, and we prove that it follows from the conjecture …