Eigenvalues of Frobenius endomorphisms of abelian varieties of low dimension

Yuri G. Zarhin

doi:10.1016/j.jpaa.2014.07.024

Eigenvalues of Frobenius endomorphisms of abelian varieties of low dimension

Yuri G. Zarhin

Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

In this paper we discuss nontrivial multiplicative relations among eigenvalues of Frobenius endomorphisms of abelian varieties over finite fields. (The trivial relations are provided by the "Riemann Hypothesis" that was proven by A. Weil.) We classify all abelian varieties over finite fields of dimension ≤3 that admit the nontrivial relations.

Original language	English (US)
Pages (from-to)	2076-2098
Number of pages	23
Journal	Journal of Pure and Applied Algebra
Volume	219
Issue number	6
DOIs	https://doi.org/10.1016/j.jpaa.2014.07.024
State	Published - Jun 1 2015

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jpaa.2014.07.024

Cite this

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AB - In this paper we discuss nontrivial multiplicative relations among eigenvalues of Frobenius endomorphisms of abelian varieties over finite fields. (The trivial relations are provided by the "Riemann Hypothesis" that was proven by A. Weil.) We classify all abelian varieties over finite fields of dimension ≤3 that admit the nontrivial relations.

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Eigenvalues of Frobenius endomorphisms of abelian varieties of low dimension

Abstract

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