Geodesic
A Horrocks-Type Theorem for Even Orthogonal $\text{K}_2$
Documenta mathematica, Tome 25 (2020), pp. 767-809.

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

We prove the Horrocks theorem for unstable even-dimensional orthogonal Steinberg groups. The Horrocks theorem for Steinberg groups is one of the principal ingredients needed for the proof of the $\text{K}_2$-analogue of Serre's problem, positive solution of which currently is only known in the linear case.
Classification : 19C20
Keywords: Steinberg group, \(\text{K}_2\)-functor, Quillen-Suslin theorem, Horrocks theorem, \(\mathbb{P}^1\)-glueing 
@article{DOCMA_2020__25__a45,
     author = {Lavrenov, Andrei V. and Sinchuk, Sergei S.},
     title = {A {Horrocks-Type} {Theorem} for {Even} {Orthogonal} {\(\text{K}_2\)}},
     journal = {Documenta mathematica},
     pages = {767--809},
     publisher = {mathdoc},
     volume = {25},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a45/}
}
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Lavrenov, Andrei V.; Sinchuk, Sergei S. A Horrocks-Type Theorem for Even Orthogonal \(\text{K}_2\). Documenta mathematica, Tome 25 (2020), pp. 767-809. http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a45/