OM representation of prime ideals and applications in function fields

Speaker: Jens Bauch

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 fA[x] a monic irreducible separable polynomial. Denote by θKsep 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 fk[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.