Lifting low-gonal curves for use in Tuitman's algorithm

Abstract: Consider a smooth projective curve $\overline{C}$ over a finite field of odd characteristic, equipped with a simply branched morphism $\overline{C} \to \PP^1$ of degree $d \leq 4$. In this article we describe how to efficiently compute a lift of $\overline{C}$ to characteristic zero, such that it can be fed as input to Tuitman's algorithm for computing the Hasse--Weil zeta function of $\overline{C}$. The full version of this paper, which is available on arXiv, also discusses the case $d=5$ over finite fields of characteristic $ >3$.

algebraic geometrynumber theory

Audience: researchers in the topic

( chat | paper | slides | video )

Comments: Chairs: Marco Streng and David Kohel

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