A Horrocks-Type Theorem for Even Orthogonal $\text{K}_2$

Andrei V. Lavrenov; Sergei S. Sinchuk

doi:10.4171/dm/762

JournalsdmVol. 25pp. 767–809

A Horrocks-Type Theorem for Even Orthogonal $K_{2}$

Andrei V. Lavrenov
Chebyshev Laboratory, St. Petersburg State University, 14th Line V.O. 29b, 199178 St. Petersburg, Russia
Sergei S. Sinchuk
Chebyshev Laboratory, St. Petersburg State University, 14th Line V.O. 29b, 199178 St. Petersburg, Russia

$A Horrocks-Type Theorem for Even Orthogonal $\text{K}_2$ cover$

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Abstract

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 $K_{2}$ -analogue of Serre's problem, positive solution of which currently is only known in the linear case.

Cite this article

Andrei V. Lavrenov, Sergei S. Sinchuk, A Horrocks-Type Theorem for Even Orthogonal $K_{2}$ . Doc. Math. 25 (2020), pp. 767–809

DOI 10.4171/DM/762