Permawound Unipotent Groups
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | |
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| _version_ | 1866909727500271616 |
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| author | Rosengarten, Zev |
| author_facet | Rosengarten, Zev |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_15605 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Permawound Unipotent Groups Rosengarten, Zev Algebraic Geometry Group Theory 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. |
| title | Permawound Unipotent Groups |
| topic | Algebraic Geometry Group Theory |
| url | https://arxiv.org/abs/2303.15605 |