An algebraic analog of the borel construction and its properties

Abstract

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.