Year: 2026
Type: preprint
Abstract: Isogeny classes of abelian varieties over finite fields were described by Tate and Honda. Deligne proved that the category of ordinary abelian varieties over a finite field is equivalent to the category of ordinary Deligne modules. Centeleghe and Stix extended Deligne's results to the whole category of abelian varieties, but, if the base finite field is not prime, then the target category is not related to Deligne modules. In this paper we introduce generalized and twisted Deligne modules and give a more direct generalization of the Deligne theorem.
Source: arXiv (Cornell University)
Author: Rybakov, Sergey
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203699153