Vol. 300, No. 2, 2019

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$J$-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
Milestones
Received: 24 September 2017
Revised: 7 August 2018
Accepted: 29 September 2018
Published: 30 July 2019
Authors
Raphaël Fino
Instituto de Matemáticas
Ciudad Universitaria (UNAM)
Mexico City
Mexico