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 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 arXiv:1006.4343
Cite
@article{arxiv.1404.5011,
title = {Categorical Bockstein sequences},
author = {Leonid Positselski},
journal= {arXiv preprint arXiv:1404.5011},
year = {2018}
}
Comments
LaTeX 2e, 60 pages; v.5: new Example 2.2, Lemma 2.5, and Remark 2.7 inserted, the proofs of Lemma 1.4(b) and of (what are now) Lemmas 2.6 and 2.8 rewritten, details added in the proofs of Lemmas 1.3(a), 1.5(b), 1.6, and 1.10, several paragraphs inserted before Lemma 0.4 and before the new Lemma 2.5, three references added; v.6: several misprints corrected -- this is intended as the final version