Lectures on bifunctors and finite generation of rational cohomology algebras

TL;DR

This paper discusses advanced concepts in functor homology, focusing on bifunctors and the finite generation of rational cohomology algebras, highlighting recent progress and conjectures related to cohomological finite generation.

Contribution

It presents a formalism related to bifunctors and explores a formality conjecture that supports the existence of universal classes in cohomology.

Findings

Proof of cohomological finite generation conjecture by Touzé

Focus on formality conjecture of Cha{\

Abstract

This text is an updated version of material used for a course at Universit\'e de Nantes, part of `Functor homology and applications', April 23-27, 2012. The proof by Touz\'e of my conjecture on cohomological finite generation (CFG) has been one of the successes of functor homology. We will not treat the original proof in any detail. Instead we will focus on a formality conjecture of Cha{\l}upnik that leads to second generation proof of the existence of the universal classes of Touz\'e.