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Global Koszul duality

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Andrey Lazarev
University of Lancaster/MPIM, Bonn
Tue, 28/01/2020 - 14:00 - 15:00
MPIM Lecture Hall

Koszul duality is a phenomenon that shows up in rational homotopy theory, deformation theory and other subfields of algebra and topology. Its modern formulation is due to the works of Hinich, Keller-Lefevre and Positselski. It is a certain correspondence between categories of differential graded (dg) algebras and conilpotent dg coalgebras; there is also a module-comodule level version of it. In this talk I explain what happens if one drops the condition of conilpotency on the coalgebra side; the consequences turn out to be quite dramatic. I will show how this non-conilpotent (or global) version of Koszul duality comes up naturally in the study of derived categories of complex algebraic manifolds and infinity local systems on topological spaces. Time permitting, I will also explain how one can construct a global version of deformation theory for certain deformation problems based on this approach. This is joint work with Ai Guan.

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