In [6, Theorem 2.2] Doi gave a Hopf-algebraic proof of a generalization of Oberst's theorem on affine quotients of affine schemes. He considered a commutative Hopf algebra H over a field, coacting on a commutative H-comodule algebra A. If AcoH denotes the subalgebra of coinvariant elements of A and β : A ⊗ Acoll A → A ⊗ H the canonical map, he proved that the following are equivalent: (a) AcoH ⊂ A is a faithfully flat Hopf Galois extension; (b) the functor (-)coH : MHA → AcoH-Mod is an equivalence; (c) A is coflat as a right H-comodule and β is surjective.
A-H-bimodules and Equivalences
MENINI, Claudia;
2001
Abstract
In [6, Theorem 2.2] Doi gave a Hopf-algebraic proof of a generalization of Oberst's theorem on affine quotients of affine schemes. He considered a commutative Hopf algebra H over a field, coacting on a commutative H-comodule algebra A. If AcoH denotes the subalgebra of coinvariant elements of A and β : A ⊗ Acoll A → A ⊗ H the canonical map, he proved that the following are equivalent: (a) AcoH ⊂ A is a faithfully flat Hopf Galois extension; (b) the functor (-)coH : MHA → AcoH-Mod is an equivalence; (c) A is coflat as a right H-comodule and β is surjective.File in questo prodotto:
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