Maps between curves and arithmetic obstructions

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.

Locations

• Contemporary mathematics - American Mathematical Society - View
• arXiv (Cornell University) - View - PDF
• DataCite API - View