Translation-Invariant Line Bundles On Linear Algebraic Groups

Abstract

We study the Picard groups of connected linear algebraic groups, and especially the subgroup of translation-invariant line bundles. We prove that this subgroup is finite over every global function field. We also utilize our study of these groups in order to construct various examples of pathological behavior for the cohomology of commutative linear algebraic groups over local and global function fields.

22 pages; this is a substantially revised and simplified version of the original version of this paper