Adele constructions of direct images of differentials and symbols

Abstract

Explicit constructions are given for certain residues and symbols from differentials and -groups of two-dimensional local fields to differentials and multiplicative groups of one-dimensional local fields. The maps obtained are used to construct the Gysin morphisms between the cohomology of the sheaves of regular differential forms and between the Chow groups in the case of a projective morphism of an algebraic surface onto an algebraic curve.