Luca Terenzi: The six functor formalism for perverse Nori motives

Abstract:

Let \(k\) be a field of characteristic zero. Conjecturally, there should exist an abelian category of mixed motives containing the universal cohomology groups of \(k\)-varieties; morphisms and extensions in this category should be deeply related to algebraic cycles. The theory of Nori motives provides an unconditional (albeit quite mysterious) candidate for such a category. The conjectural theory of mixed motives should be part of a more general theory of mixed motivic sheaves over \(k\)-varieties, governed by Grothendieck's formalism of the six operations. In the last decade there have been various attempts at extending the theory of Nori motives in this direction. After reviewing Nori's original theory in some detail, I will present the theory of perverse Nori motives, recently introduced by Ivorra–Morel. A complete six functor formalism is now available in this setting, by work of Ivorra–Morel and of myself; the final goal of my talk is to discuss the main ideas behind its construction.