Derived isogenies and isogenies for abelian surfaces
Abstract
We study twisted Fourier-Mukai partners of abelian surfaces.Following Huybrechts (2019), we introduce twisted derived equivalences (also called derived isogenies) between abelian surfaces.We show that there is a twisted derived Torelli theorem for abelian surfaces over algebraically closed fields with characteristic ̸ = 2, 3.Our approach involves extending to rational Hodge structures, ℓ-adic Tate modules and F-crystals a trick introduced by Shioda in the context of integral Hodge structures.Using this trick, we can confirm the Tate conjecture in a special case.Then we make use of Tate's isogeny theorem to give a characterization of derived isogenies between abelian surfaces via so-called principal isogenies.As a consequence, we show the two abelian surfaces are principally isogenous if and only if they are derived isogenous.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Publication details
- Journal / source
- Algebra & Number Theory
- Publisher
- Mathematical Sciences Publishers
- Volume
- 20
- Issue
- 6
- Pages
- 1185–1234
- Publication date
- 26 May 2026
- Language
- EN