Structure of Hyperbolic Unitary Groups I: Elementary Subgroups

Abstract

This is the first in a series of papers dedicated to the structure of hyperbolic unitary groups over form rings and their subgroups. In this part, we recall foundations of the theory and study the elementary subgroup of the hyperbolic unitary group over a form ring. In particular, using a variant of Suslin’s patching method, we prove standard commutator formulae for relative elementary subgroups.