Articles liés à Arthur Packets for p-adic Groups by Way of Microlocal...

Arthur Packets for p-adic Groups by Way of Microlocal Vanishing Cycles of Perverse Sheaves, with Examples - Couverture souple

Cunningham, Clifton; Fiori, Andrew; Moussaoui, Ahmed; Mracek, James; Xu, Bin

 
9781470451172: Arthur Packets for p-adic Groups by Way of Microlocal Vanishing Cycles of Perverse Sheaves, with Examples
Couverture souple
ISBN 10 : 1470451174 ISBN 13 : 9781470451172
Editeur : American Mathematical Society, 2022

Synopsis

In this article we propose a geometric description of Arthur packets for padic groups using vanishing cycles of perverse sheaves. Our approach is inspired by the 1992 book by Adams, Barbasch and Vogan on the Langlands classification of admissible representations of real groups and follows the direction indicated by Vogan in his 1993 paper on the Langlands correspondence. Using vanishing cycles, we introduce and study a functor from the category of equivariant perverse sheaves on the moduli space of certain Langlands parameters to local systems on the regular part of the conormal bundle for this variety. In this article we establish the main properties of this functor and show that it plays the role of microlocalization in the work of Adams, Barbasch and Vogan. We use this to define ABV-packets for pure rational forms of p-adic groups and propose a geometric description of the transfer coefficients that appear in Arthur's main local result in the endoscopic classification of representations. This article includes conjectures modelled on Vogan's work, including the prediction that Arthur packets are ABV-packets for p-adic groups. We gather evidence for these conjectures by verifying them in numerous examples.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l'auteur

Clifton Cunningham, University of Calgary, Canada.

Andrew Fiori, University of Lethbridge, Canada.

Ahmed Moussaoui, Universite Versailles Saint Quentin, France.

James Mracek, University of Toronto, Canada.

Bin Xu, Tsinghua University, China.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2022
Langue
anglais
ISBN 10 
1470451174
ISBN 13 
9781470451172
Reliure
Broché
Nombre de pages
209
Coordonnées du fabricant
non disponible
Personne responsable
non disponible