We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
Frobenius Distributions of Low Dimensional Abelian Varieties Over Finite Fields.
- Authors
Arango-Piñeros, Santiago; Bhamidipati, Deewang; Sankar, Soumya
- Abstract
Given a |$g$| -dimensional abelian variety |$A$| over a finite field |$\mathbf{F}_{q}$| , the Weil conjectures imply that the normalized Frobenius eigenvalues generate a multiplicative group of rank at most |$g$|. The Pontryagin dual of this group is a compact abelian Lie group that controls the distribution of high powers of the Frobenius endomorphism. This group, which we call the Serre–Frobenius group, encodes the possible multiplicative relations between the Frobenius eigenvalues. In this article, we classify all possible Serre–Frobenius groups that occur for |$g \le 3$|. We also give a partial classification for simple ordinary abelian varieties of prime dimension |$g\geq 3$|.
- Subjects
FINITE fields; LIE groups; COMPACT groups; EIGENVALUES; ABELIAN varieties; LOGICAL prediction
- Publication
IMRN: International Mathematics Research Notices, 2024, Vol 2024, Issue 16, p11989
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnae148