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Around rationality of cycles

100%

Fino R.

Open Mathematics

2013

tom 11

nr 6

1068-1077

We prove certain results comparing rationality of algebraic cycles over the function field of a quadric and over the base field. These results have already been obtained by Alexander Vishik in the case of characteristic 0, which allowed him to work with algebraic cobordism theory. Our proofs use the modulo 2 Steenrod operations in the Chow theory and work in any characteristic ≠ 2.

Variations on a theme of rationality of cycles

100%

Karpenko N.

Open Mathematics

2013

tom 11

nr 6

1056-1067

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 construction of fields of u-invariant 2r + 1, for r ≥ 3, is extended to arbitrary characteristic ≠ 2.

Ograniczanie wyników

2 Open Mathematics

1 Fino R.

1 Karpenko N.

2 2013

Wyniki wyszukiwania

Around rationality of cycles

Variations on a theme of rationality of cycles