Suppose that G is an affine algebraic group scheme faithfully flat over another affine scheme X = SpecR, H is a closed faithfully flat X-subscheme, and G/H is an affine X-scheme. In this case, we prove that the categories of left R[H]-comodules and G-equivariant vector bundles over G/H are equivalent and this equivalence respects tensor products. Our algebraic construction is based on a well-known geometric Borel construction. Bibliography: 5 titles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M.-F. Atiyah and F. Hirzebruch, “Vector bundles and homogeneous spaces,” Proc. Symp. Pure Math., 3, 7–38 (1961).
I. A. Panin, “On the algebraic K-theory of twisted flag varieties,” K-Theory, 8, No. 6, 541–585 (1994).
R. Hartshorne, Algebraic Geometry, Springer-Verlag, New York (1977).
J. S. Milne, Etale Cohomology, Princeton Mathematical Series, 33, Princeton University Press (1980).
M.-F. Atyiah and I. MacDonald, Introduction To Commutative Algebra, Eddison-Wesley Publishing Company (1969).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 394, 2011, pp. 262–293.
Rights and permissions
About this article
Cite this article
Kobyzev, I.B. An algebraic analog of the borel construction and its properties. J Math Sci 188, 621–639 (2013). https://doi.org/10.1007/s10958-013-1153-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-013-1153-8