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

### 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

## 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 $\text{K}_2$-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 $\text{K}_2$. Doc. Math. 25 (2020), pp. 767–809

DOI 10.4171/DM/762