## Abelian Varieties Multi-Site Seminar Series: Jens Bauch

• Date: 12/10/2015
Lecturer(s):
Jens Bauch, Simon Fraser University
Location:

Simon Fraser University

Topic:

OM representation of prime ideals and applications in function fields [video]

Description:

Let $A$ be a Dedekind domain, $K$ the fraction field of $A$, and $f\in A[x]$ a monic irreducible separable polynomial. Denote by $\theta\in K^{\mathrm{sep}}$ a root of $f$ and let $F=K(\theta)$ be the finite separable extension of $K$ generated by $\theta$. We consider $\mathcal{O}$ the integral closure of $A$ in $L$. For a given non-zero prime ideal $\mathfrak{p}$ of $A$ the Montes algorithm determines a parametrization (OM representation) for every prime ideal $\mathfrak{P}$ of $\mathcal{O}$ lying over $\mathfrak{p}$. For a field $k$ and $f\in k[t,x]$ 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.

Other Information:

A video of this event is available on mathtube.org

Bluejeans Connection Info:

Meeting Title: CRG: Explicit methods for abelian varieties meeting Meeting Time: Every second Thursday of the month • from November 12,
2015 • through December 10, 2015 • 11 a.m. MST / 1 hr
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