Categorical Bockstein Sequences

Abstract

We construct the reduction of an exact category with a twist functor with respect to an element of its graded center in presence of an exact-conservative forgetful functor annihilating this central element. The construction uses matrix factorizations in a nontraditional way. We obtain the Bockstein long exact sequences for the Ext groups in the exact categories produced by reduction. Our motivation comes from the theory of Artin-Tate motives and motivic sheaves with finite coefficients, and our key techniques generalize those of [13, Section 4].

Koszulity of cohomology = K(π,1)-ness + quasi-formality

“…The construction of the category G is a particular case of a general construction of the reduction of an exact category by a graded center element developed in the paper [40].…”