Vol. 15, No. 7, 2021

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Pathological behavior of arithmetic invariants of unipotent groups

Zev Rosengarten

Vol. 15 (2021), No. 7, 1593–1626
DOI: 10.2140/ant.2021.15.1593
Abstract

We show that all of the nice behavior for Tamagawa numbers, Tate–Shafarevich sets, and other arithmetic invariants of pseudoreductive groups over global function fields, proved in another work, fails in general for noncommutative unipotent groups. We also give some positive results which show that Tamagawa numbers do exhibit some reasonable behavior for arbitrary connected linear algebraic groups over global function fields.

Keywords
unipotent groups, Tamagawa numbers, linear algebraic groups, Tate–Shafarevich sets
Mathematical Subject Classification 2010
Primary: 11R58
Secondary: 11R34, 11R56, 11E99
Milestones
Received: 8 January 2019
Revised: 24 January 2020
Accepted: 19 February 2021
Published: 1 November 2021
Authors
Zev Rosengarten
Einstein Institute of Mathematics
Hebrew University of Jerusalem
Edmond J. Safra Campu
Givat Ram
Jerusalem
Israel