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arXiv · 1409.8510

Decomposing Jacobians of Curves over Finite Fields in the Absence of Algebraic Structure

Omran Ahmadi·Gary McGuire·Antonio Rojas-León
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Abstract

We consider the issue of when the L-polynomial of one curve over $\F_q$ divides the L-polynomial of another curve. We prove a theorem which shows that divisibility follows from a hypothesis that two curves have the same number of points over infinitely many extensions of a certain type, and one other assumption. We also present an application to a family of curves arising from a conjecture about exponential sums. We make our own conjecture about L-polynomials, and prove that this is equivalent to the exponential sums conjecture.

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Omran Ahmadi, Gary McGuire, Antonio Rojas-León. 2014-09-30. Decomposing Jacobians of Curves over Finite Fields in the Absence of Algebraic Structure. https://arxiv.org/abs/1409.8510

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