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 < ottmar.loos@uibk.ac.at >