2023/03/27 by Zev Rosengarten, Rosengarten, Zev · 2 citations
Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Commutative property #Finite Group Theory Research #Geometric and Algebraic Topology #Group theory #Mathematics #Pure mathematics #Quotient #Reductive group #Torsion (gastropod) #Unipotent #math.AG #math.GR
paper · pdf · doi:10.48550/arxiv.2303.15605
openalex publication_date 2023/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the class of permawound unipotent groups, and show that they simultaneously satisfy certain "ubiquity" and "rigidity" properties that in combination render them very useful in the study of general wound unipotent groups. As an illustration of their utility, we present two applications: We prove that nonsplit smooth unipotent groups over (infinite) finitely-generated fields have infinite first cohomology; and we show that every commutative p-torsion wound unipotent group over a field of degree of imperfection 1 is the maximal unipotent quotient of a commutative pseudo-reductive group, thus partially answering a question of Totaro.