Order of torsion in of quadrics.
Rost projectors and Steenrod operations.
On the group .
Variations on a theme of rationality of cycles
We prove certain weak versions of some celebrated results due to Alexander Vishik comparing rationality of algebraic cycles over the function field of a quadric and over the base field. The original proofs use Vishik’s symmetric operations in the algebraic cobordism theory and work only in characteristic 0. Our proofs use the modulo 2 Steenrod operations in the Chow theory and work in any characteristic ≠ 2. Our weak versions are still sufficient for existing applications. In particular, Vishik’s...
Torsion in CH2 of Severi-Brauer varieties and indecomposability of generic algebras.
Holes in
On standard norm varieties
Let be a prime integer and a field of characteristic . Let be theof a symbol in the Galois cohomology group (for some ), constructed in the proof of the Bloch-Kato conjecture. The main result of the paper affirms that the function field has the following property: for any equidimensional variety , the change of field homomorphism of Chow groups with coefficients in integers localized at is surjective in codimensions . One of the main ingredients of the proof is a computation of...
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