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Lifts of supersingular abelian varieties with small Mumford-Tate groups
- Publication Year :
- 2022
-
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 threefolds, can be lifted to ones isogenous to a square, respectively product, of elliptic curves. On the other hand, we show that supersingular abelian threefolds cannot be lifted to one isogenous to the cube of an elliptic curve over the Witt vectors.<br />Comment: 17 pages. Comments welcome!
- Subjects :
- Mathematics - Number Theory
Mathematics - Algebraic Geometry
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2208.07809
- Document Type :
- Working Paper