• Corpus ID: 235658743

Real points in a homogeneous space of a real algebraic group

@inproceedings{Borovoi2021RealPI,
  title={Real points in a homogeneous space of a real algebraic group},
  author={Mikhail Borovoi},
  year={2021}
}
Let G be a linear algebraic group over the field of real numbers R, and let Y be a right homogeneous space of G. We wish to find a real point of Y or to prove that Y has no real points. We describe a method to do that, implicitly using second nonabelian Galois cohomology. Our method is suitable for computer-assisted calculations. 
View PDF on arXiv
1 Citations

One Citation

Citation Type

Citation Type

Classification of real trivectors in dimension nine

References

SHOWING 1-10 OF 29 REFERENCES
Algebraic Groups and Class Fields
Summary of the main results algebraic curves maps from a curve to a commutative group singular algebraic curves generalized jacobians class field theory group extension and cohomology.
EQUIVARIANT MODELS OF SPHERICAL VARIETIES
Let G be a connected semisimple group over an algebraically closed field k of characteristic 0. Let Y = G / H be a spherical homogeneous space of G , and let Y ′ be a spherical embedding of Y . Let k…
Stably Cayley Groups in Characteristic Zero
A linear algebraic group G over a field k is called a Cayley group if it admits a Cayley map, i.e., a G-equivariant birational isomorphism over k between the group variety G and the Lie algebra…
Linear Algebraic Groups
We give a summary, without proofs, of basic properties of linear algebraic groups, with particular emphasis on reductive algebraic groups.
Reductive Group Schemes
— We develop the relative theory of reductive group schemes, using dynamic techniques and algebraic spaces to streamline the original de-
Algebraic groups and number theory
(Chapter Heading): Algebraic Number Theory. Algebraic Groups. Algebraic Groups over Locally Compact Fields. Arithmetic Groups and Reduction Theory. Adeles. Galois Cohomology. Approximation in…
NÉRON MODELS
§1.1. Motivation. The purpose of these notes is to explain the definition and basic properties of the Néron model A of an abelian variety A over a global or local field K. We also give some idea of…
Nonabelian H2 in Galois cohomology
  • In: Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965), Proc. Sympos. Pure Math. IX, pp. 164–182. Amer. Math. Soc., Providence, R.I.
  • 1966
Springer
  • “Nonabelian H2 in Galois cohomology.” In: Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965), Proc. Sympos. Pure Math. IX, pp. 164–182. Amer. Math. Soc., Providence, R.I.,
  • 1966
Real graded Lie algebras, Galois cohomology, and classification of trivectors in R^9
In this paper we classify real trivectors in dimension 9. The corresponding classification over the field C of complex numbers was done by Vinberg and Elashvili in 1978. One of the main tools used…
...
1
2
3
...