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Twisted Deligne modules and abelian varieties over finite fields

  • Sergey Rybakov
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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.

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Cite

BibTeXRIS
BibTeX
@misc{rybakov2026twisted,
  title = {{Twisted Deligne modules and abelian varieties over finite fields}},
  author = {Sergey Rybakov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.16668},
  eprint = {2608.16668},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.16668},
}
RIS
TY  - UNPB
TI  - Twisted Deligne modules and abelian varieties over finite fields
AU  - Sergey Rybakov
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2608.16668
UR  - https://arxiv.org/abs/2608.16668
AB  - 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.
ER  -