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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 **V**_{i} 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 L_{e} 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 >