Vanishing cycles for formal schemes.
Variations de structure de Hodge et zéro-cycles sur les surfaces générales.
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...
Variations on a Theorem of Abel.