Vol. 300, No. 2, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 309: 1  2
Vol. 308: 1  2
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
$J$-invariant of hermitian forms over quadratic extensions

Raphaël Fino

Vol. 300 (2019), No. 2, 375–404

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.

Hermitian and quadratic forms, grassmannians, Chow groups and motives
Mathematical Subject Classification 2010
Primary: 11E39, 14C25
Received: 24 September 2017
Revised: 7 August 2018
Accepted: 29 September 2018
Published: 30 July 2019
Raphaël Fino
Instituto de Matemáticas
Ciudad Universitaria (UNAM)
Mexico City