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Working paper

Categorical Bockstein sequences

arxiv.org. math. Cornell University, 2014. No. 1404.5011.
Positselski L.
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 procedure allows, e.g., to recover the abelian/exact category of modular representations of a finite group from the exact category of its l-adic representations. 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 Section 4 in the author's paper "Mixed Artin-Tate motives with finite coefficients".