Regular supercuspidal representations

T Kaletha - Journal of the American Mathematical Society, 2019 - ams.org
We show that, in good residual characteristic, most supercuspidal representations of a
tamely ramified reductive $ p $-adic group $ G $ arise from pairs $(S,\theta) $, where $ S $ is …

[PDF][PDF] Weakly commensurable arithmetic groups and isospectral locally symmetric spaces

G Prasad, A Rapinchuk - Publications Mathématiques de l'IHÉS, 2009 - numdam.org
The goal of this paper is two-fold. First, we introduce and analyze a new relationship
between (Zariski-dense) abstract subgroups of the groups of F-rational points of two …

Sur la classification des schémas en groupes semi-simples

P Gille - Panoramas et synthèses, 2016 - hal.science
Résumé We deal with the classification of semisimple group schemes via the Bruhat-Tits'
presentation of non-abelian cohomology. The goal is to generalize Galois techniques to …

Generic elements in Zariski-dense subgroups and isospectral locally symmetric spaces

G Prasad, AS Rapinchuk - Thin groups and superstrong …, 2014 - books.google.com
The article contains a survey of our results on length-commensurable and isospectral locally
symmetric spaces and of related problems in the theory of semisimple algebraic groups. We …

Isometries of quadratic spaces.

E Bayer-Fluckiger - … of the European Mathematical Society (EMS …, 2015 - content.ems.press
Let k be a global field of characteristic not 2, and let f∈ k [X] be an irreducible polynomial.
We show that a non-degenerate quadratic space has an isometry with minimal polynomial f …

Tame Tori in p-Adic Groups and Good Semisimple Elements

J Fintzen - International Mathematics Research Notices, 2021 - academic.oup.com
Let be a reductive group over a non-archimedean local field. We provide necessary
conditions and sufficient conditions for all tori of to split over a tamely ramified extension of …

[PDF][PDF] Embeddings of maximal tori in orthogonal groups

E Bayer-Fluckiger - Annales de l'Institut Fourier, 2014 - numdam.org
Embeddings of maximal tori in orthogonal groups Page 1 ANNA L E S D E L’INSTITU T FO
U RIER ANNALES DE L’INSTITUT FOURIER Eva BAYER-FLUCKIGER Embeddings of …

Simple algebraic groups with the same maximal tori, weakly commensurable Zariski-dense subgroups, and good reduction

VI Chernousov, AS Rapinchuk, IA Rapinchuk - Advances in Mathematics, 2024 - Elsevier
We provide a new condition for an absolutely almost simple algebraic group to have good
reduction with respect to a discrete valuation of the base field which is formulated in terms of …

Weakly commensurable S-arithmetic subgroups in almost simple algebraic groups of types B and C

S Garibaldi, A Rapinchuk - Algebra & Number Theory, 2013 - msp.org
Let G 1 and G 2 be absolutely almost simple algebraic groups of types B ℓ and C ℓ,
respectively, defined over a number field K. We determine when G 1 and G 2 have the same …

On maximal tori of algebraic groups of type G2

C Beli, P Gille, TY Lee - Pacific Journal of Mathematics, 2015 - msp.org
On maximal tori of algebraic groups of type G2 Page 1 Pacific Journal of Mathematics ON
MAXIMAL TORI OF ALGEBRAIC GROUPS OF TYPE G2 CONSTANTIN BELI, PHILIPPE GILLE …