Cosheaves of Steinberg pro-groups

E. Yu. Voronetsky

Saint Petersburg State University

Abstract: Steinberg pro-groups are certain pro-groups used to analyze ordinary Steinberg groups locally in Zariski topology. In this paper we show that Steinberg pro-groups associated with general linear groups, odd unitary groups, and Chevalley groups satisfy a Zariski cosheaf property as crossed pro-modules over the base groups. Also, we prove an analogue of the standard commutator formulae for relative Steinberg groups.

Key words and phrases: Steinberg groups, pro-groups, crossed squares.

UDC: 512.747

Received: 03.02.2025