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arXiv · 1709.05734

Maps between curves and arithmetic obstructions

Andrew V. Sutherland·Jose Felipe Voloch
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Abstract

Let X and Y be curves over a finite field. In this article we explore methods to determine whether there is a rational map from Y to X by considering L-functions of certain covers of X and Y and propose a specific family of covers to address the special case of determining when X and Y are isomorphic. We also discuss an application to factoring polynomials over finite fields.

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Andrew V. Sutherland, Jose Felipe Voloch. 2017-09-18. Maps between curves and arithmetic obstructions. https://doi.org/10.1090/conm%2F722%2F14532

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