$J$-invariant of hermitian forms over quadratic extensions

Raphaël Fino

Vol. 300 (2019), No. 2, 375–404

DOI: 10.2140/pjm.2019.300.375

Abstract

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.

Keywords

Hermitian and quadratic forms, grassmannians, Chow groups and motives

Mathematical Subject Classification 2010

Primary: 11E39, 14C25

Milestones

Received: 24 September 2017

Revised: 7 August 2018

Accepted: 29 September 2018

Published: 30 July 2019