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arXiv · 1602.04079

$J$-invariant of hermitian forms over quadratic extensions

Raphaël Fino
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Abstract

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 hermitan 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.

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Raphaël Fino. 2016-02-12. $J$-invariant of hermitian forms over quadratic extensions. https://doi.org/10.2140/pjm.2019.300.375

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