J-INVARIANT OF HERMITIAN FORMS OVER QUADRATIC EXTENSIONS

摘要

We develop a version of the J-invariant for hermitian forms over quadratic extensions using a similar method to Alexander Vishik's approach using quadratic forms. This discrete invariant contains information about rationality of algebraic cycles on the maximal unitary grassmannian associated with a hermitian form over a quadratic extension. The computation of the canonical 2-dimension of this grassmannian in terms of the J-invariant is provided, as well as a complete motivic decomposition.