Seminario Teoría de Números UAM-ICMAT
THE LOCAL EPSILON CONSTANT CONJECTURE FOR UNRAMIFIED TWISTS OF Zp(1)
SPEAKER: Werner Bley (Ludwig-Maximilians-Universität, Munich)
DATE & TIME: Tuesday, 09th April 2019 - 11:30
VENUE: Aula 420, Módulo 17, Departamento de Matemáticas, UAM
ORGANISER: UAM - ICMAT
ABSTRACT: Let N/K be a finite Galois extension of p-adic number fields. We will give an explicit reformulation of the equivariant local epsilon constant conjecture, formulated previously by various authors (Kato, Benois and Berger, Fukaya and Kato and others), in the special case of certain 1-dimensional unramified twists of Zp(1). In joint work with A.Cobbe we have shown the validity of this conjecture for certain wildly and weakly ramified abelian extensions N/K.
Comparing the twisted conjecture to a conjecture of Breuning we obtain an explicit conjectural description of a certain Euler characteristic related to local fundamental classes which already occurs in the formulation of Chinburg's Ω2-conjecture. This part of the talk concerns joint work in progress with D.Burns.