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arXiv · 1907.06225

Pathological Behavior of Arithmetic Invariants of Unipotent Groups

Zev Rosengarten
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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.

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Zev Rosengarten. 2019-07-14. Pathological Behavior of Arithmetic Invariants of Unipotent Groups. https://doi.org/10.2140/ant.2021.15.1593

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