#### Vol. 300, No. 2, 2019

 Recent Issues Vol. 304: 1 Vol. 303: 1  2 Vol. 302: 1  2 Vol. 301: 1  2 Vol. 300: 1  2 Vol. 299: 1  2 Vol. 298: 1  2 Vol. 297: 1  2 Online Archive Volume: Issue:
 The Journal Editorial Board Subscriptions Officers Special Issues Submission Guidelines Submission Form Contacts ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Author Index To Appear Other MSP Journals
$J$-invariant of hermitian forms over quadratic extensions

### Raphaël Fino

Vol. 300 (2019), No. 2, 375–404
##### 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