On a generalization of Grothendieck's theorem

2006/05/17 by Bachuki Mesablishvili, Mesablishvili, Bachuki
Mathematics · #16W30 #18C15 #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.math/0605470

openalex publication_date 2006/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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