Pathological Behavior of Arithmetic Invariants of Unipotent Groups
arXiv:1907.06225 · 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 pseudo-reductive groups over global function fields proved in \cite{rospred} fails in general for non-commutative 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.
37 pages; This is the second half of a preprint arXiv:1806.10723 submitted earlier; we have broken it up in order to make the arXiv versions conform to the published ones