Quadratic Forms, Linear Algebraic Groups, and Cohomology PDF Download

Author: Skip Garibaldi
Publisher: Springer Science & Business Media
ISBN: 1441962115
Category : Mathematics
Languages : en
Pages : 344

View

Book Description
Developments in Mathematics is a book series devoted to all areas of mathematics, pure and applied. The series emphasizes research monographs describing the latest advances. Edited volumes that focus on areas that have seen dramatic progress, or are of special interest, are encouraged as well.

Author: Tsit-Yuen Lam
Publisher: Addison-Wesley
ISBN: 9780805356663
Category : Mathematics
Languages : en
Pages : 344

View

Book Description

Author: Richard S. Elman
Publisher: American Mathematical Soc.
ISBN: 9780821873229
Category : Mathematics
Languages : en
Pages : 456

View

Book Description
This book is a comprehensive study of the algebraic theory of quadratic forms, from classical theory to recent developments, including results and proofs that have never been published. The book is written from the viewpoint of algebraic geometry and includes the theory of quadratic forms over fields of characteristic two, with proofs that are characteristic independent whenever possible. For some results both classical and geometric proofs are given. Part I includes classical algebraic theory of quadratic and bilinear forms and answers many questions that have been raised in the early stages of the development of the theory. Assuming only a basic course in algebraic geometry, Part II presents the necessary additional topics from algebraic geometry including the theory of Chow groups, Chow motives, and Steenrod operations. These topics are used in Part III to develop a modern geometric theory of quadratic forms.

Author:
Publisher: World Scientific
ISBN:
Category :
Languages : en
Pages : 1191

View

Book Description

Author: Rajendra Bhatia
Publisher: World Scientific
ISBN: 9814462934
Category : Mathematics
Languages : en
Pages : 4137

View

Book Description
ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.

Author: Eva Bayer-Fluckiger
Publisher: American Mathematical Soc.
ISBN: 0821827790
Category : Mathematics
Languages : en
Pages : 330

View

Book Description
This volume outlines the proceedings of the conference on "Quadratic Forms and Their Applications" held at University College Dublin. It includes survey articles and research papers ranging from applications in topology and geometry to the algebraic theory of quadratic forms and its history. Various aspects of the use of quadratic forms in algebra, analysis, topology, geometry, and number theory are addressed. Special features include the first published proof of the Conway-Schneeberger Fifteen Theorem on integer-valued quadratic forms and the first English-language biography of Ernst Witt, founder of the theory of quadratic forms.

Author: Ricardo Baeza
Publisher: American Mathematical Soc.
ISBN: 0821846485
Category : Mathematics
Languages : en
Pages : 424

View

Book Description
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.

Author: Fabien Morel
Publisher: Springer
ISBN: 3642295142
Category : Mathematics
Languages : en
Pages : 267

View

Book Description
This text deals with A1-homotopy theory over a base field, i.e., with the natural homotopy theory associated to the category of smooth varieties over a field in which the affine line is imposed to be contractible. It is a natural sequel to the foundational paper on A1-homotopy theory written together with V. Voevodsky. Inspired by classical results in algebraic topology, we present new techniques, new results and applications related to the properties and computations of A1-homotopy sheaves, A1-homology sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties.

Author:
Publisher: World Scientific
ISBN: 9814324353
Category :
Languages : en
Pages : 814

View

Book Description

Author: Jakob Stix
Publisher: Springer
ISBN: 3642306748
Category : Mathematics
Languages : en
Pages : 257

View

Book Description
The section conjecture in anabelian geometry, announced by Grothendieck in 1983, is concerned with a description of the set of rational points of a hyperbolic algebraic curve over a number field in terms of the arithmetic of its fundamental group. While the conjecture is still open today in 2012, its study has revealed interesting arithmetic for curves and opened connections, for example, to the question whether the Brauer-Manin obstruction is the only one against rational points on curves. This monograph begins by laying the foundations for the space of sections of the fundamental group extension of an algebraic variety. Then, arithmetic assumptions on the base field are imposed and the local-to-global approach is studied in detail. The monograph concludes by discussing analogues of the section conjecture created by varying the base field or the type of variety, or by using a characteristic quotient or its birational analogue in lieu of the fundamental group extension.