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Unramified cohomology of classifying varieties for classical simply connected groups

Alexander Merkurjev — 2002

Annales scientifiques de l'École Normale Supérieure

Degree three cohomological invariants of semisimple groups

Alexander Merkurjev — 2016

Journal of the European Mathematical Society

We study the degree 3 cohomological invariants with coefficients in $ℚ / ℤ (2)$ of a semisimple group over an arbitrary field. A list of all invariants of adjoint groups of inner type is given.

R-equivalence and rationality problem for semisimple adjoint classical algebraic groups

Alexander S. Merkurjev — 1996

Publications Mathématiques de l'IHÉS

On standard norm varieties

Nikita A. Karpenko; Alexander S. Merkurjev — 2013

Annales scientifiques de l'École Normale Supérieure

Let $p$ be a prime integer and $F$ a field of characteristic $0$ . Let $X$ be theof a symbol in the Galois cohomology group $H^{n + 1} (F, μ_{p}^{\otimes n})$ (for some $n \geq 1$ ), constructed in the proof of the Bloch-Kato conjecture. The main result of the paper affirms that the function field $F (X)$ has the following property: for any equidimensional variety $Y$ , the change of field homomorphism $CH (Y) \to CH (Y_{F (X)})$ of Chow groups with coefficients in integers localized at $p$ is surjective in codimensions $< (dim X) / (p - 1)$ . One of the main ingredients of the proof is a computation of...

Rost projectors and Steenrod operations.

Karpenko, Nikita; Merkurjev, Alexander — 2002

Documenta Mathematica

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