Frobenius distributions of low dimensional abelian varieties over finite fields
| Autor: | Arango-Piñeros, Santiago, Bhamidipati, Deewang, Sankar, Soumya |
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| Rok vydání: | 2023 |
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| Zdroj: | International Mathematics Research Notices 2024 (2024), no. 16, 11989-12020 |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $g>3$. Comment: Fixed typesetting bug from v3 |
| Databáze: | arXiv |
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