On curves over finite fields with Jacobians of small exponent

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We show that finite fields over which there is a curve of a given genus g with its Jacobian having a small exponent, are very rare. This extends a recent result of W. Duke in the case g=1. We also show when g=1 or g=2 that our bounds are best possible.
V3. Small corrections; references updated

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Number Theory, 11G20; 14H40

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http://salesiana.dossiersoluciones.com/handle/123456789/173282

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0607474
 http://arxiv.org/abs/math/0607474
 Int. J. Number Theory 4 (2008), 819-826

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arXiv