HIGHER HIDA THEORY and p-ADIC L-FUNCTIONS for GSp4

David Loeffler; Vincent Pilloni; Christopher Skinner; Sarah Livia Zerbes

doi:10.1215/00127094-2021-0049

HIGHER HIDA THEORY and p-ADIC L-FUNCTIONS for GSp4

David Loeffler
, Vincent Pilloni
, Christopher Skinner
, Sarah Livia Zerbes

Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We use the "higher Hida theory" recently introduced by the second author to p-adically interpolate periods of nonholomorphic automorphic forms for GSp4, contributing to coherent cohomology of Siegel threefolds in positive degrees. We apply this new method to construct p-adic L-functions associated to the degree-4 (spin) L-function of automorphic representations of GSp4, and the degree-8 L-function of GSp4 xGL2.

Original language	English (US)
Pages (from-to)	4033-4121
Number of pages	89
Journal	Duke Mathematical Journal
Volume	170
Issue number	18
DOIs	https://doi.org/10.1215/00127094-2021-0049
State	Published - Dec 1 2022

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1215/00127094-2021-0049

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AU - Loeffler, David

AU - Pilloni, Vincent

AU - Skinner, Christopher

AU - Zerbes, Sarah Livia

PY - 2022/12/1

Y1 - 2022/12/1

N2 - We use the "higher Hida theory" recently introduced by the second author to p-adically interpolate periods of nonholomorphic automorphic forms for GSp4, contributing to coherent cohomology of Siegel threefolds in positive degrees. We apply this new method to construct p-adic L-functions associated to the degree-4 (spin) L-function of automorphic representations of GSp4, and the degree-8 L-function of GSp4 xGL2.

AB - We use the "higher Hida theory" recently introduced by the second author to p-adically interpolate periods of nonholomorphic automorphic forms for GSp4, contributing to coherent cohomology of Siegel threefolds in positive degrees. We apply this new method to construct p-adic L-functions associated to the degree-4 (spin) L-function of automorphic representations of GSp4, and the degree-8 L-function of GSp4 xGL2.

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UR - https://www.scopus.com/pages/publications/85122147544#tab=citedBy

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DO - 10.1215/00127094-2021-0049

M3 - Article

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SP - 4033

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JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

IS - 18

ER -

HIGHER HIDA THEORY and p-ADIC L-FUNCTIONS for GSp4

Abstract

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