Discriminants and Arakelov Euler characteristics
by
Ted Chinburg
University of Pennsylvania
Coauthors: Martin Taylor, George Pappas

In this talk I will discuss joint work with Martin Taylor and George Pappas on two different Galois structure invariants of the de Rham cohomology of projective schemes over Z. These invariants take into account Quillen metrics at infinity and the pairings provided by Serre duality, respectively. Each invariant determines, and is determined by, root numbers associated to the given group action on a scheme. The fact that the invariants are (essentially) equal generalizes to schemes the fact that the covolume of a ring of integers in the product of its archimedean completions is a power of two times the square root of the absolute value of a discriminant.

Date received: March 18, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caew-36.