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2020 Supersingular locus of Hilbert modular varieties, arithmetic level raising and Selmer groups
Yifeng Liu, Yichao Tian
Algebra Number Theory 14(8): 2059-2119 (2020). DOI: 10.2140/ant.2020.14.2059

Abstract

This article has three goals: First, we generalize the result of Deuring and Serre on the characterization of supersingular locus to all Shimura varieties given by totally indefinite quaternion algebras over totally real number fields. Second, we generalize the result of Ribet on arithmetic level raising to such Shimura varieties in the inert case. Third, as an application to number theory, we use the previous results to study the Selmer group of certain triple product motive of an elliptic curve, in the context of the Bloch–Kato conjecture.

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Yifeng Liu. Yichao Tian. "Supersingular locus of Hilbert modular varieties, arithmetic level raising and Selmer groups." Algebra Number Theory 14 (8) 2059 - 2119, 2020. https://doi.org/10.2140/ant.2020.14.2059

Information

Received: 22 October 2018; Revised: 30 September 2019; Accepted: 26 March 2020; Published: 2020
First available in Project Euclid: 12 November 2020

MathSciNet: MR4172702
Digital Object Identifier: 10.2140/ant.2020.14.2059

Subjects:
Primary: 14G35
Secondary: 11G05 , 11R34

Keywords: automorphic forms , Hilbert modular varieties , level raising , Selmer groups , Supersingular locus

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.14 • No. 8 • 2020
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