Serre conjecture II for pseudo-reductive groups
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917324347408384 |
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| author | Nguyen, Mac Nam Trung |
| author_facet | Nguyen, Mac Nam Trung |
| contents | The Serre conjecture II predicts that every torsor under a semisimple, simply connected, algebraic group over a field of cohomological dimension at most 2 and of degree of imperfection at most 1 has a rational point. We generalize this conjecture to pseudo-reductive groups and prove their equivalence. In particular, we show that every torsor under a pseudo-semisimple, simply connected group over a global function field or a non-archimedean local field always has a rational point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08061 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Serre conjecture II for pseudo-reductive groups Nguyen, Mac Nam Trung Number Theory Algebraic Geometry Primary 14L10, Secondary 11E72, 14G17 The Serre conjecture II predicts that every torsor under a semisimple, simply connected, algebraic group over a field of cohomological dimension at most 2 and of degree of imperfection at most 1 has a rational point. We generalize this conjecture to pseudo-reductive groups and prove their equivalence. In particular, we show that every torsor under a pseudo-semisimple, simply connected group over a global function field or a non-archimedean local field always has a rational point. |
| title | Serre conjecture II for pseudo-reductive groups |
| topic | Number Theory Algebraic Geometry Primary 14L10, Secondary 11E72, 14G17 |
| url | https://arxiv.org/abs/2603.08061 |