Saved in:
Bibliographic Details
Main Authors: Geldhauser, Nikita, Petrov, Victor
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