Eigenvalues of Frobenius endomorphisms of abelian varieties of low dimension

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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 languageEnglish (US)
Pages (from-to)2076-2098
Number of pages23
JournalJournal of Pure and Applied Algebra
Volume219
Issue number6
DOIs
StatePublished - Jun 1 2015

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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