On the construction of the trace in Serre duality

Abstract

The object of this lecture is to construct this diagram in the chain level, in the case Y is a complete intersection of arbitrary codimension. To this purpose, we represent local cohomology clases of X by semi-meromorphic forms with poles in the union U(Y1:1 ≤ 1 ≤ n), and define the trace by means of the residual currents introduced in (2) and (3).