Faithfully flat descent of abelian categories

DOI10.1080/00927877908822395zbMath0415.18009OpenAlexW2168507647MaRDI QIDQ3050616

Mitsuhiro Takeuchi

Publication date: 1979

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927877908822395

zbMATH Keywords

commutative ringabelian categorynonabelian cohomologyBrauer groupfaithfully flat extension2-nd cohomology of Villamayor-ZelinskyAzumaya R-algebraset of descent data

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) (13D03) Abelian categories, Grothendieck categories (18E10) Brauer groups of schemes (14F22) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Representation theory of associative rings and algebras (16Gxx)

Related Items

Ext//ad(SpR,\(mu^ A)\)=Br(A/k)

Cites Work

• On groups \(H^n(S/R)\) related to the Amitsur cohomology and the Brauer group of commutative rings
• Brauer groups and Amitsur cohomology for general commutative ring extensions