| Résume | Let $k$ be a field of characteristic 0. As envisioned by Grothendieck, Beilinson, Deligne, and others, there should exist an abelian category of mixed motives over $k$ defining the universal $\mathbb{Q}$-linear cohomology theory for algebraic $k$-varieties. The existence of the category of mixed motives is still conjectural; however, in the 1990's an abelian category carrying (in a suitable sense) a universal cohomology theory for $k$-varieties was constructed unconditionally by M. Nori.
In the last decade, there have been several attempts at extending Nori's construction to a theory of motivic sheaves endowed with a six functor formalism. After reviewing Nori's theory in some detail, I will present the theory of perverse Nori motives introduced by F. Ivorra and S. Morel. By work of Ivorra--Morel and of myself, a complete six functor formalism is now available in this setting; the final goal of my talk is to sketch the main ideas behind its construction. |
