Bernstein Eigenvarieties

We construct parabolic analogues of (global) eigenvarieties, of patched eigenvarieties and of (local) trianguline varieties, that we call, respectively, Bernstein eigenvarieties, patched Bernstein eigenvarieties, and Bernstein paraboline varieties. We study the geometry of these rigid analytic space...

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Bibliographic Details
Published inPeking mathematical journal (Online) Vol. 7; no. 2; pp. 471 - 642
Main Authors Breuil, Christophe, Ding, Yiwen
Format Journal Article
LanguageEnglish
Published Singapore Springer Nature Singapore 01.09.2024
Springer
Subjects
Mathematics
Mathematics and Statistics
Original Article
Eigenvariety
Galois representation
Automorphic representation
Companion constituent
22E50
Bernstein center
Parabolic group
11S23
22E35
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Summary:We construct parabolic analogues of (global) eigenvarieties, of patched eigenvarieties and of (local) trianguline varieties, that we call, respectively, Bernstein eigenvarieties, patched Bernstein eigenvarieties, and Bernstein paraboline varieties. We study the geometry of these rigid analytic spaces, in particular (generalising results of Breuil–Hellmann–Schraen) we show that their local geometry can be described by certain algebraic schemes related to the generalised Grothendieck–Springer resolution. We deduce several local–global compatibility results, including a classicality result (with no trianguline assumption at p ), and new cases towards the locally analytic socle conjecture of Breuil in the non-trianguline case.
ISSN:2096-6075
2524-7182
2524-7182
DOI:10.1007/s42543-023-00062-8