Pathological behavior of arithmetic invariants of unipotent groups

Zev Rosengarten*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.

Original languageEnglish
Pages (from-to)1593-1626
Number of pages34
JournalAlgebra and Number Theory
Volume15
Issue number7
DOIs
StatePublished - 2021

Bibliographical note

Publisher Copyright:
© 2021 Mathematical Sciences Publishers.

Keywords

  • Linear algebraic groups
  • Tamagawa numbers
  • Tate–Shafarevich sets
  • Unipotent groups

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