RaphaŽl Fino: J-invariant of hermitian forms over quadratic extensions


Submission: 2016, Feb 23, revised: 2017, Apr 20

We develop the version of the J-invariant for hermitian forms over quadratic extensions in a similar way Alexander Vishik did it for quadratic forms.This discrete invariant contains informations 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.

2010 Mathematics Subject Classification: 14C25 ; 11E39

Keywords and Phrases: Hermitian and quadratic forms, grassmannians, Chow groups and motives

Full text: dvi.gz 56 k, dvi 130 k, ps.gz 873 k, pdf.gz 243 k, pdf 272 k.

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