This book introduces various notions defined in graded terms extending the notions most frequently used as basic ingredients in the theory of Azumaya algebras: separability and Galois extensions of commutative rings, crossed products and Galois cohomology, Picard groups, and the Brauer group.
This book introduces various notions defined in graded terms extending the notions most frequently used as basic ingredients in the theory of Azumaya algebras: separability and Galois extensions of commutative rings, crossed products and Galois cohomology, Picard groups, and the Brauer group.
Generalized Crossed Products Graded Ring Theory Generalized Crossed Products Some Results on Commutative Graded Rings Arithmetically Graded Rings Separability and Graded Galois Extensions Graded Completion and Henselization The Join of gr-Henselian Rings Graded Brauer Groups and the Crossed Product Theorems Graded Faithfully Flat Descent Projective Graded Modules Grothendieck and Picard Groups of Graded Rings Brauer Groups of Graded Rings Graded Cohomology Groups and the Crossed Product Theorem Application to Some Special Cases Brauer Groups of Graded Fields Brauer Groups of gr-Local Rings The Brauer Group of a Graded Ring Modulo a Graded Ideal Brauer Groups of Regular Graded Rings Etale Cohomology for Graded Rings Cohomology on the gr-Etale Site Hypercoverings and Verdier's Refinement Theorem Application to the Graded Brauer Group A Graded Version of Gabber's Theorem The Villamayor-Zelinsky Approach Applications The Brauer-Long Group The Brauer-Wall Group Graded Brauer Groups in a Geometrical Context References
Generalized Crossed Products Graded Ring Theory Generalized Crossed Products Some Results on Commutative Graded Rings Arithmetically Graded Rings Separability and Graded Galois Extensions Graded Completion and Henselization The Join of gr-Henselian Rings Graded Brauer Groups and the Crossed Product Theorems Graded Faithfully Flat Descent Projective Graded Modules Grothendieck and Picard Groups of Graded Rings Brauer Groups of Graded Rings Graded Cohomology Groups and the Crossed Product Theorem Application to Some Special Cases Brauer Groups of Graded Fields Brauer Groups of gr-Local Rings The Brauer Group of a Graded Ring Modulo a Graded Ideal Brauer Groups of Regular Graded Rings Etale Cohomology for Graded Rings Cohomology on the gr-Etale Site Hypercoverings and Verdier's Refinement Theorem Application to the Graded Brauer Group A Graded Version of Gabber's Theorem The Villamayor-Zelinsky Approach Applications The Brauer-Long Group The Brauer-Wall Group Graded Brauer Groups in a Geometrical Context References
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