Abstract Stefan Wewers

Stefan Wewers will speak on

L-function of curves and semistable reduction

Abstract: Let Y be a smooth projective curve over a number field K. The Hasse-Weil L-function L(Y,s) is conjectured to have an analytic continuation and a functional equation. In order to test this conjecture numerically it is necessary to compute L(Y,s) explicity. Since L(Y,s) is defined as an Euler product, this amounts to computing all local L-factors. For primes of good reduction, this can be done by point counting. The computation at primes of bad reduction is much more involved.

In my talk I will explain how the local L-factor and the corresponding exponent of the conductor at a prime p depend on the semistable reduction of Y at p. Then I will report on recent progress at computing semistabel reduction explictly. This is joint work with Irene Bouw, Kai Arzdorf, Michel Börner and Julian Rüth.