Quadratic Forms--algebra, Arithmetic, And Geometry: Algebraic And Arithmetic Theory Of Qudratic Forms, December 13 - 19, 2007 Frutillar, Chile (contemporary Mathematics)

This volume presents a collection of articles that are based on talks delivered at the International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms held in Frutillar, Chile in December 2007. The theory of quadratic forms is closely connected with a broad spectrum of areas in algebra and number theory. The articles in this volume deal mainly with questions from the algebraic, geometric, arithmetic, and analytic theory of quadratic forms, and related questions in algebraic group theory and algebraic geometry. Contents 8 Preface 10 List of Participants 12 H1(X, ν) of conics and Witt kernels in characteristic 2 14 Pythagoras numbers and quadratic field extensions 34 On perfection relations in lattices 42 Linear independence of local densities of quadratic forms and its application to the theory of Siegel modular forms 64 Representation of reduced special groups in algebras of continous functions 96 Solubility of Fermat equations 112 Multiplicative properties of integral binary quadratic forms 120 Effective structure theorems for symplectic spaces via height 130 Orthogonal involutions on algebras of degree 16 and the Killing form of E8 (with an appendix by Kirill Zainoulline) 144 The first Zariski cohomology group of the Witt sheaf over a split simply connected simple algebraic group 176 On families of testing formulae for a pp formula 194 Siegel modular forms of small weight and the Witt operator 202 On isotropy of quadratic pairs 224 Specialization of forms in the presence of characteristic 2: first steps 232 Representation of integers by special positive definite integral quadratic forms 256 Hyper-isotropy of bilinear forms in characteristic 2 262 A historical view of the Pythagoras numbers of fields 284 The extensions of R-places and application 302 Essential dimension 312 On the Pfister number of quadratic forms 340 Martin Kneser’s work on quadratic forms and algebraic groups 352 Enumerating perfect forms 372 Reduction mod l of Theta Series of Level ln 392 On a reciprocity theorem of Gauss 404 A bound of the number of reduced Arakelov divisors of a number field 412 This Volume Presents A Collection Of Articles That Are Based On Talks Delivered At The International Conference On The Algebraic And Arithmetic Theory Of Quadrutic Forms Held In Frutillar, Chile In December 2007. The Theory Of Quadratic Forms Is Closely Connected With A Broad Spectrum Of Arenas In Algebra And Number Theory. The Articles In This Volume Deal Mainly With Questions From The Algebraic, Geometric, Arithmetic, And Analytic Theory Of Quadratic Forms, And Related Questions In Algebraic Group Theory And Algebraic Geometry.--jacket. Ricardo Baeza ... [et Al.], Editors. Includes Bibliographical References.