Bounds for Completely Decomposable Jacobians

Details Bounds for Completely Decomposable Jacobians Bounds for Completely Decomposable Jacobians

2010-07-20

arxiv.org/abs/1007.3344v1

Finite fields with applications to coding theory, cryptography and related areas (Oaxaca, 2001), 86--93, Springer, Berlin, 200

Mathematics

Number Theory

9 pages, first appeared in 2002, posted for greater accessibility, with an addendum on X(11) mod 2

Scientific paper

A curve over the field of two elements with completely decomposable Jacobian is shown to have at most six rational points and genus at most 26. The bounds are sharp. The previous upper bound for the genus was 145. We also show that a curve over the field of $q$ elements with more than $q^{m/2}+1$ rational points has at least one Frobenius angle in the open interval $(\pi/m,3\pi/m)$. The proofs make use of the explicit formula method.

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