Sylvester theorem for certain free modules
We discuss here the conjectures of Kaplansky and of Lam concerning the ii-univariant of a field of characteristic different from two. Both conjectures are shown t.o hold true for any field having at most 32 square classes.
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...