Geodesic
Subtle Characteristic Classes and Hermitian Forms
Documenta mathematica, Tome 24 (2019), pp. 2493-2523.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Following \textit{A. Smirnov} and \textit{A. Vishik} [``Subtle characteristic classes'', Preprint, \url{arXiv:1401.6661v1}], we compute the motivic cohomology ring of the Nisnevich classifying space of the unitary group associated to the standard split hermitian form of a quadratic extension. This provides us with subtle characteristic classes which take value in the motivic cohomology of the Čech simplicial scheme associated to a hermitian form. Comparing these new classes with subtle Stiefel-Whitney classes arising in the orthogonal case, we obtain relations among the latter ones holding in the motivic cohomology of the Čech simplicial scheme associated to a quadratic form divisible by a 1-fold Pfister form. Moreover, we present a description of the motive of the torsor corresponding to a hermitian form in terms of its subtle characteristic classes.
Classification : 11E39, 14F42, 20G15, 55R40
Keywords: Hermitian forms, motivic cohomology, Nisnevich classifying space, characteristic classes 
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     author = {Tanania, Fabio},
     title = {Subtle {Characteristic} {Classes} and {Hermitian} {Forms}},
     journal = {Documenta mathematica},
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     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a3/}
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Tanania, Fabio. Subtle Characteristic Classes and Hermitian Forms. Documenta mathematica, Tome 24 (2019), pp. 2493-2523. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a3/