Algebra/topology seminar

Speaker: Sergio Estrada

Title: A Zariski-local notion of F-Total Acyclicity for complexes of sheaves

Abstract: We study a notion of total acyclicity for complexes of flat sheaves
over a scheme. It is Zariski-local, i.e. it can be verified on any open affine
covering of the scheme. We recover, and in several cases extend the
validity of, recent theorems on existence of covers and precovers in categories of
sheaves. One consequence is the existence of an adjoint to the inclusion of these
totallyacyclic complexes into the homotopy category of complexes of flat sheaves.

The talk is based on a joint work with Lars Winther Christensen and
Alina Iacob.