Brauer Groups and the Cohomology of Graded Rings 0824779789, 9780824779788

This book introduces various notions defined in graded terms extending the notions most frequently used as basic ingredi

151 47 2MB

English Pages 280 Year 1988

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Brauer Groups and the Cohomology of Graded Rings
0824779789, 9780824779788

Author / Uploaded
Stefaan Caenepeel
Freddy Van Oystaeyen

Table of contents :
Cover
Half Title
Series Page
Title Page
Copyright Page
Preface
Contents
I. Generalized Crossed Products
I.1 Graded Ring Theory
I.2 Generalized Crossed Products
II. Some Results On Commutative Rings Graded
II.1 Arithmetically Graded Rings
Il.2 Separability and Graded Galois Extensions
II.3 Graded Completion and Henselization
II.4 The Join of gr-Henselian Rings
III. Graded Brauer Groups And The Crossedproduct Theorems
III.1 Graded Faithfully Flat Descent
III.2 Projective Graded Modules
III.3 Grothendieck and Picard Groups of Graded Rings
III.4 Brauer Groups of Graded Rings
III.5 Graded Cohomology Groups and the Crossed Product Theorem
IV. Application To Some Special Cases
IV.1 Brauer Groups of Graded Fields
IV.2 Brauer Groups of gr-Local Rings
IV.3 The Brauer Group of a Graded Ring Modulo a Graded Ideal
IV.4 Brauer Groups of Regular Graded Rings
V. Etale Cohomology For Graded Rings
V.1 Cohomology on the gr-Etale Site
V.2 Hypercoverings and Verdier's Refinement Theorem
V.3 Application to the Graded Brauer Group
V.4 A Graded Version of Gabber's Theorem
V.5 The Villamayor-Zelinsky Approach
VI. Application
VI.1 The Brauer-Long Group
VI.2 The Brauer-Wall Group
VI.3 Graded Brauer Groups in a Geometrical Context
References
Index

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