Endoscopy on SL2-eigenvarieties
Artikel i vetenskaplig tidskrift, 2024

In this paper, we study p -adic endoscopy on eigenvarieties for <> SL 2 \mathrm{SL}_{2} over totally real fields, taking a geometric perspective. We show that non-automorphic members of endoscopic L -packets of regular weight contribute eigenvectors to overconvergent cohomology at critically refined endoscopic points on the eigenvariety, and we precisely quantify this contribution. This gives a new perspective on and generalizes previous work of the second author. Our methods are geometric, and are based on showing that the <> SL 2 \mathrm{SL}_{2} -eigenvariety is locally a quotient of an eigenvariety for <> GL 2 \mathrm{GL}_{2}, which allows us to explicitly describe the local geometry of the <> SL 2 \mathrm{SL}_{2} -eigenvariety. In particular, we show that it often fails to be Gorenstein.

Författare

Christian Johansson

Chalmers, Matematiska vetenskaper, Algebra och geometri

Judith Ludwig

Universität Heidelberg

Journal fur die Reine und Angewandte Mathematik

00754102 (ISSN) 14355345 (eISSN)

Vol. In Press

Ämneskategorier

Algebra och logik

Subatomär fysik

Jämförande språkvetenskap och allmän lingvistik

Gastroenterologi

Matematisk analys

DOI

10.1515/crelle-2024-0026

Mer information

Senast uppdaterat

2024-06-14