On a localization formula of epsilon factors via microlocal geometry

Abstract

Given a lisse l-adic sheaf G on a smooth proper variety X and a lisse sheaf F on an open dense U in X, Kato and Saito conjectured a localization formula for the global l-adic epsilon factor εl(X,F ⊗ G) in terms of the global epsilon factor of F and a certain intersection number associated to det(G) and the Swan class of F . In this article, we prove an analog of this conjecture for global de Rham epsilon factors in the classical setting of DX -modules on smooth projective varieties over a field of characteristic zero.