Pathological behavior of arithmetic invariants of unipotent groups

Rosengarten, Zev

doi:10.2140/ant.2021.15.1593

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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

Vol. 15, No. 7, 2021