Resumen de Around rationality of integral cycles

Raphaël Fino

• In this article we prove a result comparing rationality of integral algebraic cycles over the function field of a quadric and over the base field. This is an integral version of the result known for Z/2Z-coefficients. Those results have already been proved 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.