LocalL-factors of motives and regularized determinants

Abstract

For a smooth projective variety X over a global field k consider the completed L-function of H w(x). It is defined as the Euler product over all places v of k of the local L-factors L~(Hw(X), s) introduced in [Se]. In the function field case the generalized Lefschetz trace formula in /-adic cohomology gives a global cohomological expression for the L-function. This has been used on the following purposes: