Quadratic Forms, Linear Algebraic Groups, and Cohomology

1. Front Matter

   Pages i-x

   PDF

2. Surveys

   1. Front Matter

      Pages 1-1

      PDF

   2. Multiples of forms

      • Eva Bayer-Fluckiger

      Pages 3-11

   3. On Saltman’s p-Adic Curves Papers

      • Eric Brussel

      Pages 13-39

   4. Serre’s Conjecture II: A Survey

      • Philippe Gille

      Pages 41-56

   5. Field Patching, Factorization, and Local–Global Principles

      • Daniel Krashen

      Pages 57-82

   6. Deformation Theory and Rational Points on Rationally Connected Varieties

      • Max Lieblich

      Pages 83-108

   7. Recent Progress on the Kato Conjecture

      • Shuji Saito

      Pages 109-124

   8. Elliptic Curves and Iwasawa’s µ = 0 Conjecture

      • R. Sujatha

      Pages 125-135

   9. Cohomological Invariants of Central Simple Algebras with Involution

      • Jean-Pierre Tignol

      Pages 137-171

   10. Witt Groups of Varieties and the Purity Problem

       • Kirill Zainoulline

       Pages 173-185

3. Invited Articles

   1. Front Matter

      Pages 187-187

      PDF

4. Invited articles

   1. Some Extensions and Applications of the Eisenstein Irreducibility Criterion

      • Anuj Bishnoi, Sudesh K. Khanduja

      Pages 189-197

   2. On the Kernel of the Rost Invariant for E ₈ Modulo 3

      • Vladimir Chernousov

      Pages 199-214

   3. Une version du théorème d’Amer et Brumer pour les zéro-cycles

      • Jean-Louis Colliot-Thélène, Marc Levine

      Pages 215-223

   4. Quaternion Algebras with the Same Subfields

      • Skip Garibaldi, David J. Saltman

      Pages 225-238

   5. Lifting of Coefficients for Chow Motives of Quadrics

      • Olivier Haution

      Pages 239-247

   6. Upper Motives of Outer Algebraic Groups

      • Nikita A. Karpenko

      Pages 249-257

   7. Triality and étale algebras

      • Max-Albert Knus, Jean-Pierre Tignol

      Pages 259-286

   8. Remarks on Unimodular Rows

      • N. Mohan Kumar, M. Pavaman Murthy

      Pages 287-293

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.

• Algebraic Geometry
• Algebraic Number Theory
• Cohomology
• Field Patching
• ICM 2010
• Iwasawa Theory
• K-Theory
• Linear Algebraic Groups
• Number theory
• Quadratic Forms
• Raman Parimala
• Serre's Conjecture
• linear algebra
• p-adic Curves

• CNRS, Labo. Mathématiques, Université Paris-Sud XI, Orsay CX, France

  Jean-Louis Colliot-Thélène

• Dept. Mathematics &, Computer Science, Emory University, Atlanta, USA

  Skip Garibaldi

• School of Mathematics, Tata Institute of Fundamental Research, Mumbai, India

  R. Sujatha

• Dept. Mathematics & Statistics, University of Hyderabad, Hyderabad, India

  Venapally Suresh

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