Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.10969 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929466154942464 |
|---|---|
| author | Geldhauser, Nikita Petrov, Victor |
| author_facet | Geldhauser, Nikita Petrov, Victor |
| contents | We show a Springer type theorem for the variety of parabolic subgroups of type $1,2,6$ for all groups of type $E_6$. As far as we know this gives the first example for the validity of the Springer theorem for projective homogeneous varieties of type $^2E_6$ different from varieties of Borel subgroups. The proof combines several topics, notably the Rost invariant, a Tits construction, Cartan's symmetric spaces and indirectly the structure of the Chow motives of projective homogeneous varieties of exceptional type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10969 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tits construction and Rost invariant Geldhauser, Nikita Petrov, Victor Algebraic Geometry We show a Springer type theorem for the variety of parabolic subgroups of type $1,2,6$ for all groups of type $E_6$. As far as we know this gives the first example for the validity of the Springer theorem for projective homogeneous varieties of type $^2E_6$ different from varieties of Borel subgroups. The proof combines several topics, notably the Rost invariant, a Tits construction, Cartan's symmetric spaces and indirectly the structure of the Chow motives of projective homogeneous varieties of exceptional type. |
| title | Tits construction and Rost invariant |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2408.10969 |