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Translation-Invariant Line Bundles On Linear Algebraic Groups
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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.
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Quasi-Isometric Bounded Generation by ${\mathbb Q}$-Rank-One Subgroups
Every arithmetic and S-arithmetic subgroup of an isotropic almost-simple Q-group is quasi-isometrically boundedly generated by standard Q-rank-one subgroups.
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