Eigenvalues of Frobenius endomorphisms of abelian varieties of low dimension

• Yuri G. Zarhin ^[1]
  1. [1] Pennsylvania State University

     Pennsylvania State University

     Borough of State College, Estados Unidos

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 6 (June 2015), 2015, págs. 2076-2098
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.07.024
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• Resumen

  • 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.