On curves over finite fields with Jacobians of small exponent

Details On curves over finite fields with Jacobians of small exponent On curves over finite fields with Jacobians of small exponent

2006-07-19

arxiv.org/abs/math/0607474v3

Int. J. Number Theory 4 (2008), 819-826

Mathematics

Number Theory

V3. Small corrections; references updated

Scientific paper

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.

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