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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Translation-invariant line bundles on linear algebraic groups

Author: Zev Rosengarten
Journal: J. Algebraic Geom. 30 (2021), 433-455
Published electronically: March 16, 2020
MathSciNet review: 4283548
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Abstract | References | Additional Information

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.

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Additional Information

Zev Rosengarten
Affiliation: Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, 91904, Jerusalem, Israel

Received by editor(s): January 3, 2019
Received by editor(s) in revised form: January 27, 2019, August 5, 2019, August 14, 2019, and January 31, 2020
Published electronically: March 16, 2020
Additional Notes: While completing this work, the author was supported by an ARCS Scholar Award, a Ric Weiland Graduate Fellowship, and a Zuckerman Postdoctoral Scholarship.
Article copyright: © Copyright 2020 University Press, Inc.