OM representation of prime ideals and applications in function fields
Date: Thu, Dec 10, 2015
Location: PIMS, Simon Fraser University
Conference: PIMS CRG in Explicit Methods for Abelian Varieties
Subject: Mathematics, Number Theory
Class: Scientific
Abstract:
Let A be a Dedekind domain, K the fraction field of A, and f∈A[x] a monic irreducible separable polynomial. Denote by θ∈Ksep a root of f and let F=K(θ) be the finite separable extension of K generated by θ. We consider O the integral closure of A in L. For a given non-zero prime ideal p of A the Montes algorithm determines a parametrization (OM representation) for every prime ideal P of O lying over p. For a field k and f∈k[t,x] this yields a new representation of places of the function field F/k determined by f. In this talk we summarize some applications which improve the arithmetic in the divisor class group of F using this new representation.