Bifunctors and universal cohomology classes

The category of strict polynomial bifunctors over the field $\Bbb F_p$ has an interesting homological algebra.

There are surprising formulas that describe the effect of Frobenius twist on certain Ext groups. We will explain some of this.

The bifunctor theory has been crucial in the construction by Antoine Touz\'e of `universal' cohomology classes needed in the proof of my cohomological finite generation conjecture: If a reductive algebraic group $G$ defined over a field $k$ acts algebraically via algebra automorphisms on a finite type commutative $k$-algebra, then the graded $k$-algebra $H^*(G,A)$ is finitely generated.

Recall that the subring $H^0(G,A)$ of invariants in $A$ was already known to be finitely generated by Mumford-Nagata-Haboush.