Lifts of Supersingular Abelian Varieties With Small Mumford–Tate Groups
Creators
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1.
Institut des Hautes Études Scientifiques
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2.
California Institute of Technology
Abstract
We investigate to what extent an abelian variety over a finite field can be lifted to one in characteristic zero with small Mumford–Tate group. We prove that supersingular abelian surfaces, respectively three-folds, can be lifted to ones isogenous to a square, respectively product, of elliptic curves. On the other hand, we show that supersingular abelian three-folds cannot be lifted to one isogenous to the cube of an elliptic curve over the Witt vectors.
Copyright and License
© The Author(s) 2023. Published by Oxford University Press.
This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/pages/standard-publication-reuse-rights)
Acknowledgement
It is a pleasure to thank Ananth Shankar for asking us this question and to Ananth Shankar and Padma Srinivasan for several invaluable conversations. Y.H.J.L. is grateful to IHÉS for a wonderful atmosphere. A.O. thanks Caltech, Pasadena, and IAS, Princeton, for excellent working conditions. We are extremely grateful to the anonymous referees for their thorough reading and for their many suggestions that have helped improve the exposition.
Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2208.07809 (arXiv)
Dates
- Accepted
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2023-10-11
- Available
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2023-10-31Published online