Addendum to: Finiteness theorems for discrete subgroups of bounded covolume in semi-simple groups. (English) Zbl 0712.11026

Borel, Armand; Prasad, Gopal

Publ. Math., Inst. Hautes Étud. Sci. 71, 173-177 (1990).

If G is an anisotropic outer form of type A, defined over a global function field k, then there is a separable quadratic extension \(\ell\) of k and a central division algebra \({\mathcal D}\), over \(\ell\), with an involution \(\sigma\) of the second kind such that either \[ G(k)=\{d\in {\mathcal D}^{\times}| d\sigma (d)=1\text{ and } Nrd(d)=1\} \] or there exists an anisotropic hermitian form h on \({\mathcal D}^ 2\), defined in terms of the involution \(\sigma\), such that \(G=SU(h)\). Due to an oversight, in the proof of Theorem 7.3 of [ibid. 69, 119-171 (1989; Zbl 0707.11032)] the groups k-isomorphic to SU(h), where h is as above, were not considered. Here it is shown that in fact these groups need to be excluded from the purview of the theorem.

MSC:

11F06	Structure of modular groups and generalizations; arithmetic groups
20G25	Linear algebraic groups over local fields and their integers
22E40	Discrete subgroups of Lie groups

Keywords:

linear algebraic groups; arithmetic groups

Citations:

Zbl 0631.20033; Zbl 0707.11032