STNB 2013 (27è Any)

Genus computation of global function fields


Jens Bauch


In this talk 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 $k_0$ 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 $[k_0:k]$ 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.


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