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On a generalization of Grothendieck's theorem

Bachuki Mesablishvili
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Abstract

A wide generalization of the classical theorem of A. Grothendieck asserting that for any faithfully flat extension of commutative rings, the corresponding relative Picard group and the Amitsur 1-cohomology group with values in the units-functor are isomorphic, is obtained. This implies some known results that are concerned with extending to non-commutative rings of Grothendieck's theorem.

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Bachuki Mesablishvili. 2006-05-17. On a generalization of Grothendieck's theorem. https://arxiv.org/abs/math/0605470

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