Maps between curves and arithmetic obstructions
Andrew V. Sutherland, Jose Felipe Voloch

TL;DR
This paper investigates methods to determine the existence of rational maps between curves over finite fields using L-functions and covers, with applications to polynomial factorization.
Contribution
It introduces a new approach using L-functions of covers to detect rational maps and proposes a specific family of covers for testing isomorphism between curves.
Findings
L-functions can indicate the existence of rational maps between curves
A new family of covers helps determine curve isomorphism
Application to polynomial factorization over finite fields
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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