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Supersingular locus of
Hilbert modular varieties, arithmetic level raising and
Selmer groups
Yifeng Liu and Yichao Tian |
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Vol. 14 (2020), No. 8, 2059–2119
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DOI: 10.2140/ant.2020.14.2059
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Abstract |
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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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Keywords
Hilbert modular varieties, supersingular locus, automorphic
forms, level raising, Selmer groups
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Mathematical Subject Classification 2010
Primary: 14G35
Secondary: 11G05, 11R34
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Milestones
Received: 22 October 2018
Revised: 30 September 2019
Accepted: 26 March 2020
Published: 18 September 2020
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Authors |
| Yifeng Liu | |
| Department of Mathematics Yale University New Haven, CT United States |
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| Yichao Tian | |
| UFR de mathématique et de
l’informatique IRMA, University of Strasbourg France |
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