Quadratic Forms, Linear Algebraic Groups, and Cohomology (Developments in Mathematics (18)) (English and French Edition)

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. Surveys -- Multiples Of Forms -- On Saltman’s P-adic Curves Papers -- Serre’s Conjecture Ii: A Survey -- Field Patching, Factorization, And Local–global Principles -- Deformation Theory And Rational Points On Rationally Connected Varieties -- Recent Progress On The Kato Conjecture -- Elliptic Curves And Iwasawa’s µ = 0 Conjecture -- Cohomological Invariants Of Central Simple Algebras With Involution -- Witt Groups Of Varieties And The Purity Problem -- Invited Articles -- Some Extensions And Applications Of The Eisenstein Irreducibility Criterion -- On The Kernel Of The Rost Invariant For E8 Modulo 3 -- Une Version Du Théorème D’amer Et Brumer Pour Les Zéro-cycles -- Quaternion Algebras With The Same Subfields -- Lifting Of Coefficients For Chow Motives Of Quadrics -- Upper Motives Of Outer Algebraic Groups -- Triality And étale Algebras -- Remarks On Unimodular Rows -- Vector Bundles Generated By Sections And Morphisms To Grassmannians -- Adams Operations And The Brown-gersten-quillen Spectral Sequence -- Non-self-dual Stably Free Modules -- Homotopy Invariance Of The Sheaf Wnis And Of Its Cohomology -- Imbedding Quasi-split Groups In Isotropic Groups. Edited By Jean-louis Colliot-thélène ... [et Al.]. Papers From A Conference, Held Dec. 30, 2008-jan. 4, 2009 At The University Of Hyderabad, India, In Celebration Of Professor Raman Parimala's 60th Birthday. Includes Bibliographical References. 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. Surveys -- Multiples Of Forms -- On Saltman’s P-adic Curves Papers -- Serre’s Conjecture Ii: A Survey -- Field Patching, Factorization, And Local–global Principles -- Deformation Theory And Rational Points On Rationally Connected Varieties -- Recent Progress On The Kato Conjecture -- Elliptic Curves And Iwasawa’s μ = 0 Conjecture -- Cohomological Invariants Of Central Simple Algebras With Involution -- Witt Groups Of Varieties And The Purity Problem -- Invited Articles -- Some Extensions And Applications Of The Eisenstein Irreducibility Criterion -- On The Kernel Of The Rost Invariant For E8 Modulo 3 -- Une Version Du Théorème D’amer Et Brumer Pour Les Zéro-cycles -- Quaternion Algebras With The Same Subfields -- Lifting Of Coefficients For Chow Motives Of Quadrics -- Upper Motives Of Outer Algebraic Groups -- Triality And étale Algebras -- Remarks On Unimodular Rows -- Vector Bundles Generated By Sections And Morphisms To Grassmannians -- Adams Operations And The Brown-gersten-quillen Spectral Sequence -- Non-self-dual Stably Free Modules -- Homotopy Invariance Of The Sheaf Wnis And Of Its Cohomology -- Imbedding Quasi-split Groups In Isotropic Groups. Edited By Jean-louis Colliot-thélène ... [et Al.]. Papers From A Conference, Held Dec. 30, 2008-jan. 4, 2009 At The University Of Hyderabad, India, In Celebration Of Professor Raman Parimala's 60th Birthday. Includes Bibliographical References. 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 On the Kernel of the Rost Invariant for E 8 Modulo 3....Pages 199-214 Une version du théorème d’Amer et Brumer pour les zéro-cycles....Pages 215-223 Quaternion Algebras with the Same Subfields....Pages 225-238 Lifting of Coefficients for Chow Motives of Quadrics....Pages 239-247 Upper Motives of Outer Algebraic Groups....Pages 249-257 Triality and étale algebras....Pages 259-286 Remarks on Unimodular Rows....Pages 287-293 Vector Bundles Generated by Sections and Morphisms to Grassmannians....Pages 295-303 Adams Operations and the Brown-Gersten-Quillen Spectral Sequence....Pages 305-313 Non-self-dual Stably Free Modules....Pages 315-324 Front Matter....Pages 187-187 Homotopy Invariance of the Sheaf W Nis and of Its Cohomology....Pages 325-335 Imbedding Quasi-split Groups in Isotropic Groups....Pages 337-348