Degree 2 cohomological invariants of linear algebraic groups

An algorithm for computing invariants of linear actions of algebraic groups up to a given degree

We propose an algorithm for computing invariant rings of algebraic groups which act linearly on affine space, provided that degree bounds for the generators are known. The groups need not be finite nor reductive, in particular, the algorithm does not use a Reynolds operator. If an invariant ring is not finitely generated the algorithm can be used to compute invariants up to a given degree.

On Certain Cohomological Invariants of Algebraic Number Fields

We see the Poincaré series from a cohomological point of view and apply the idea to a finite group G acting on any commutative ring R with unity. For a 1cocycle c of G on the unit group R×, we define a |G|-torsion module Mc/Pc, which is independent of the choice of representatives of the cohomology class γ = [c]. We are mostly interested in determining Mc/Pc where G is the Galois group of a fin...

Cohomological Invariants of Central Simple Algebras of Degree 4

In this paper, we prove a result of Rost, which describes the cohomological invariants of central simple algebras of degree 4 with values in μ2 when the base field contains a square root of −1.

Motivic construction of cohomological invariants

The norm varieties and the varieties with special correspondences play a major role in the proof of the Bloch-Kato Conjecture by M. Rost and V. Voevodsky. In the present paper we show that a variety which possesses a special correspondence is a norm variety. As an unexpected application we give a positive answer to a problem of J.-P. Serre about groups of type E8 over Q. Apart from this we incl...

Linear Algebraic Groups