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This article is available for purchase or by subscription. See below.
Abstract
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We develop a version of the
-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
-dimension of this grassmannian
in terms of the
-invariant
is provided, as well as a complete motivic decomposition.
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Keywords
Hermitian and quadratic forms, grassmannians, Chow groups
and motives
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Mathematical Subject Classification 2010
Primary: 11E39, 14C25
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Milestones
Received: 24 September 2017
Revised: 7 August 2018
Accepted: 29 September 2018
Published: 30 July 2019
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