Ebook: Quadratic Forms, Linear Algebraic Groups, and Cohomology

This volume of invited works collects the most recent research and developments in quadratic forms, linear algebraic groups, and cohomology; topics that are each at the intersection of algebra, number theory and algebraic geometry. The contributions to this volume are the work of renowned experts and present new results related to the research of Raman Parimala, to whom this collection is dedicated. Some specific topics presented in this volume include, Iwasawa theory, Witt groups and sheafs, Chow motives, quaternion algebras, p-adic curves, and progress on the Kato conjecture as well as topics of recent interest such as field patching and a proof of the Serre's Conjecture II for function fields of complex surfaces. This volume is intended for researchers and graduate students specializing in algebra, number theory, and algebraic geometry and may be suitable for supplementary use in an advanced graduate course.

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This volume of invited works collects the most recent research and developments in quadratic forms, linear algebraic groups, and cohomology; topics that are each at the intersection of algebra, number theory and algebraic geometry. The contributions to this volume are the work of renowned experts and present new results related to the research of Raman Parimala, to whom this collection is dedicated. Some specific topics presented in this volume include, Iwasawa theory, Witt groups and sheafs, Chow motives, quaternion algebras, p-adic curves, and progress on the Kato conjecture as well as topics of recent interest such as field patching and a proof of the Serre's Conjecture II for function fields of complex surfaces. This volume is intended for researchers and graduate students specializing in algebra, number theory, and algebraic geometry and may be suitable for supplementary use in an advanced graduate course.

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This volume of invited works collects the most recent research and developments in quadratic forms, linear algebraic groups, and cohomology; topics that are each at the intersection of algebra, number theory and algebraic geometry. The contributions to this volume are the work of renowned experts and present new results related to the research of Raman Parimala, to whom this collection is dedicated. Some specific topics presented in this volume include, Iwasawa theory, Witt groups and sheafs, Chow motives, quaternion algebras, p-adic curves, and progress on the Kato conjecture as well as topics of recent interest such as field patching and a proof of the Serre's Conjecture II for function fields of complex surfaces. This volume is intended for researchers and graduate students specializing in algebra, number theory, and algebraic geometry and may be suitable for supplementary use in an advanced graduate course.
Content:
Front Matter....Pages i-x
Front Matter....Pages 1-1
Multiples of forms....Pages 3-11
On Saltman’s p-Adic Curves Papers....Pages 13-39
Serre’s Conjecture II: A Survey....Pages 41-56
Field Patching, Factorization, and Local–Global Principles....Pages 57-82
Deformation Theory and Rational Points on Rationally Connected Varieties....Pages 83-108
Recent Progress on the Kato Conjecture....Pages 109-124
Elliptic Curves and Iwasawa’s µ = 0 Conjecture....Pages 125-135
Cohomological Invariants of Central Simple Algebras with Involution....Pages 137-171
Witt Groups of Varieties and the Purity Problem....Pages 173-185
Front Matter....Pages 187-187
Some Extensions and Applications of the Eisenstein Irreducibility Criterion....Pages 189-197
Une version du th?or?me d’Amer et Brumer pour les z?ro-cycles....Pages 199-214
Quaternion Algebras with the Same Subfields....Pages 215-223
Lifting of Coefficients for Chow Motives of Quadrics....Pages 225-238
Upper Motives of Outer Algebraic Groups....Pages 239-247
Triality and ?tale algebras....Pages 249-257
Remarks on Unimodular Rows....Pages 259-286
Vector Bundles Generated by Sections and Morphisms to Grassmannians....Pages 287-293
Adams Operations and the Brown-Gersten-Quillen Spectral Sequence....Pages 295-303
Non-self-dual Stably Free Modules....Pages 305-313
Front Matter....Pages 315-324
Imbedding Quasi-split Groups in Isotropic Groups....Pages 187-187
....Pages 325-335