Weil numbers generated by other Weil numbers and torsion fields of abelian varieties

2005/04/03 by Emmanuel Kowalski, Kowalski, Emmanuel
Mathematics · #11G10 #11G20 #11G25 #11N36 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G10 #msc:11G20 #msc:11G25 #msc:11N36

paper · pdf · doi:10.48550/arxiv.math/0504042

13 pages

arxiv created 2005/04/03 · arxiv updated 2009/12/01

Abstract

Using properties of the Frobenius eigenvalues, we show that, in a precise sense, ``most'' isomorphism classes of (principally polarized) simple abelian varieties over a finite field are characterized up to isogeny by the sequence of their division fields, and a similar result for ``most'' isogeny classes. Some global cases are also treated.

Related

• Variations in the distribution of principally polarized abelian varieties among isogeny classes
• Polarizations on abelian varieties
• Weil polynomials of abelian varieties over finite fields with many rational points
• Weil polynomials of abelian varieties over finite fields
• Isogeny Classes of Abelian Varieties over Finite Fields in the LMFDB