Remarks on Holger P. Petersson's ``Idempotent 2-by-2 matrices''

We expand on the last result in H. P. Petersson's preprint in case of an arbitrary base ring instead of a field. Let Vi be the open subscheme of X consisting of all elementary idempotent matrices whose i-th row is unimodular. These subschemes form an open covering of X, and Petersson's line bundle Le generates the subgroup of the Picard group of X consisting of those line bundles which are trivial over this open covering.

Ottmar Loos < >