Genus computation of global function fields
Number Theory
2012-09-27 v3 Algebraic Geometry
Abstract
In this paper we present an algorithm that computes the genus of a global function field. Let F/k be function field over a field k, and let k0 be the full constant field of F/k. By using lattices over subrings of F, we can express the genus g of F in terms of [k0 : k] and the indices of certain orders of the finite and infinite maximal orders of F . If k is a finite field, the Montes algorithm computes the latter indices as a by-product. This leads us to a fast computation of the genus of global function fields. Our algorithm does not require the computation of any basis, neither of finite nor infinite maximal order.
Keywords
Cite
@article{arxiv.1209.0309,
title = {Genus computation of global function fields},
author = {Jens-Dietrich Bauch},
journal= {arXiv preprint arXiv:1209.0309},
year = {2012}
}