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Parabolic eigenvarieties via overconvergent cohomology
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Barrera Salazar, Daniel and Williams, Christopher David (2021) Parabolic eigenvarieties via overconvergent cohomology. Mathematische Zeitschrift, 299 . pp. 961-995. doi:10.1007/s00209-021-02707-9 ISSN 0025-5874.
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Official URL: https://doi.org/10.1007/s00209-021-02707-9
Abstract
Let G be a connected reductive group over Q such that G = G/Qp is quasi-split, and let Q ⊂ G be a parabolic subgroup. We introduce parahoric overconvergent cohomology groups with respect to Q, and prove a classicality theorem showing that the small slope parts of these groups coincide with those of classical cohomology. This allows the use of overconvergent cohomology at parahoric, rather than Iwahoric, level, and provides flexible lifting theorems that appear to be particularly well-adapted to arithmetic applications. When Q is a Borel, we recover the usual theory of overconvergent cohomology, and our classicality theorem gives a stronger slope bound than in the existing literature. We use our theory to construct Q-parabolic eigenvarieties, which parametrise p-adic families of systems of Hecke eigenvalues that are finite slope at Q, but that allow infinite slope away from Q.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
Library of Congress Subject Headings (LCSH): | Eigenfunctions, Cohomology operations, Parabolic operators | |||||||||
Journal or Publication Title: | Mathematische Zeitschrift | |||||||||
Publisher: | Springer | |||||||||
ISSN: | 0025-5874 | |||||||||
Official Date: | October 2021 | |||||||||
Dates: |
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Volume: | 299 | |||||||||
Page Range: | pp. 961-995 | |||||||||
DOI: | 10.1007/s00209-021-02707-9 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Open Access (Creative Commons) | |||||||||
Date of first compliant deposit: | 15 January 2021 | |||||||||
Date of first compliant Open Access: | 13 July 2021 | |||||||||
RIOXX Funder/Project Grant: |
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