Proceedings of the London Mathematical Society



Equivariant Epsilon Constants, Discriminants and Étale Cohomology


W. Bley a1 and D. Burns a2
a1 Institut für Mathematik, Universität Augsburg, Universitätsstrasse 8, D-86135 Augsburg, Germany. E-mail: bley@math.uni-augsburg.de
a2 Department of Mathematics, King's College London, Strand, London WC2R 2LS. E-mail: david.burns@kcl.ac.uk

Article author query
bley w   [Google Scholar] 
burns d   [Google Scholar] 
 

Abstract

Let $L/K$ be a finite Galois extension of number fields. We formulate and study a conjectural equality between an element of the relative algebraic K-group $K_0(\mathbb{Z}[\mathrm{Gal}(L/K)], \mathbb{R})$ which is constructed from the equivariant Artin epsilon constant of $L/K$ and a sum of structural invariants associated to $L/K$. The precise conjecture is motivated by the requirement that a special case of the equivariant refinement of the Tamagawa Number Conjecture of Bloch and Kato (as formulated by Flach and the second-named author) should be compatible with the functional equation of the associated L-function. We show that, more concretely, our conjecture also suggests a completely systematic refinement of the central approach and results of classical Galois module theory. In particular, the evidence for our conjecture that we present here already strongly refines many of the main results of Galois module theory.

(Received April 11 2001)
(Revised November 7 2002)


Key Words: L-functions; Tamagawa numbers; Chinburg conjectures.

Maths Classification

11R29; 11R33; 11R42.