Local-global principle for groups of type An over semi global fields
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910508472336384 |
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| author | Suresh, V. |
| author_facet | Suresh, V. |
| contents | Let F be the function field of a curve over a complete discretely valued field K. Let G be a semisimple simply connected linear algebraic group over F of type An. We give a description of the obstruction to local global principle for principal homogeneous spaces under G over F with respect to discrete valuations of F in terms of R-equivalence classes of G over some suitable over fields. Using this description we prove that this obstruction vanishes under some conditions on the residue field K. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00726 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local-global principle for groups of type An over semi global fields Suresh, V. Algebraic Geometry Number Theory 11E72, 12G05, 14G05 (primary) 14H25, 20G15, 14G27 (secondary) Let F be the function field of a curve over a complete discretely valued field K. Let G be a semisimple simply connected linear algebraic group over F of type An. We give a description of the obstruction to local global principle for principal homogeneous spaces under G over F with respect to discrete valuations of F in terms of R-equivalence classes of G over some suitable over fields. Using this description we prove that this obstruction vanishes under some conditions on the residue field K. |
| title | Local-global principle for groups of type An over semi global fields |
| topic | Algebraic Geometry Number Theory 11E72, 12G05, 14G05 (primary) 14H25, 20G15, 14G27 (secondary) |
| url | https://arxiv.org/abs/2407.00726 |