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Journal of the London Mathematical Society 2006 74(2):273-288; doi:10.1112/S0024610706023040
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© The London Mathematical Society 2006

WEIL NUMBERS GENERATED BY OTHER WEIL NUMBERS AND TORSION FIELDS OF ABELIAN VARIETIES

Emmanuel Kowalski

Université Bordeaux I A2X, 351 cours de la Libération, 33405 Talence cedex, France emmanuel.kowalski{at}math.u-bordeaux1.fr

Received 9 November 2004. Revision received 15 November 2005.

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 we show a similar result for ‘most’ isogeny classes. Some global cases are also treated.


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