Victor Buchstaber (Steklov Mathematical Institute)
buchstab@mendeleevo.ru
A unipotent algebraic group is a subgroup of the group of upper-triangular matrices determined by a system of algebraic equations. Such groups arise naturally in many branches of mathematics. Our interest to them is motivated by applications in stable homotopy theory.
We aim to compare the cohomology of a unipotent group with the cohomology of the discrete group of its points over the algebraic closure of the prime field.
We show that the canonical map from the cohomology of an unipotent algebraic group to the cohomology of the corresponding discrete group has a dense image. The kernel of this map is described explicitly in terms of the action of the Frobenius endomorphism.
This is a joint work with A. Lazarev.