Author :
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 38,53 MB
Release : 2004
Category : Forms, Pfister
ISBN : 9783540207283
Author : Oleg T. Izhboldin
Publisher : Springer
Page : 198 pages
File Size : 44,29 MB
Release : 2004-02-07
Category : Mathematics
ISBN : 3540409904
The geometric approach to the algebraic theory of quadratic forms is the study of projective quadrics over arbitrary fields. Function fields of quadrics have been central to the proofs of fundamental results since the 1960's. Recently, more refined geometric tools have been brought to bear on this topic, such as Chow groups and motives, and have produced remarkable advances on a number of outstanding problems. Several aspects of these new methods are addressed in this volume, which includes an introduction to motives of quadrics by A. Vishik, with various applications, notably to the splitting patterns of quadratic forms, papers by O. Izhboldin and N. Karpenko on Chow groups of quadrics and their stable birational equivalence, with application to the construction of fields with u-invariant 9, and a contribution in French by B. Kahn which lays out a general framework for the computation of the unramified cohomology groups of quadrics and other cellular varieties.
Author : Oleg T Tignol Jean-Pierre Izhboldin
Publisher : Springer
Page : 212 pages
File Size : 45,98 MB
Release : 2014-01-15
Category :
ISBN : 9783662177747
Author : Richard S. Elman
Publisher : American Mathematical Soc.
Page : 456 pages
File Size : 46,2 MB
Release : 2008-07-15
Category : Mathematics
ISBN : 9780821873229
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 : Oleg Tomovich Izhboldin
Publisher :
Page : 0 pages
File Size : 24,30 MB
Release : 2004
Category :
ISBN :
Author :
Publisher :
Page : 0 pages
File Size : 21,14 MB
Release : 2004
Category : Algebraic fields
ISBN :
Author : Tsit-Yuen Lam
Publisher : Addison-Wesley
Page : 344 pages
File Size : 15,87 MB
Release : 1980
Category : Mathematics
ISBN : 9780805356663
Author : Ben Andrews
Publisher : Springer Science & Business Media
Page : 306 pages
File Size : 21,23 MB
Release : 2011
Category : Mathematics
ISBN : 3642162851
This book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds, and Perelman's noncollapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem.
Author : Mak Trifković
Publisher : Springer Science & Business Media
Page : 206 pages
File Size : 32,50 MB
Release : 2013-09-14
Category : Mathematics
ISBN : 1461477174
By focusing on quadratic numbers, this advanced undergraduate or master’s level textbook on algebraic number theory is accessible even to students who have yet to learn Galois theory. The techniques of elementary arithmetic, ring theory and linear algebra are shown working together to prove important theorems, such as the unique factorization of ideals and the finiteness of the ideal class group. The book concludes with two topics particular to quadratic fields: continued fractions and quadratic forms. The treatment of quadratic forms is somewhat more advanced than usual, with an emphasis on their connection with ideal classes and a discussion of Bhargava cubes. The numerous exercises in the text offer the reader hands-on computational experience with elements and ideals in quadratic number fields. The reader is also asked to fill in the details of proofs and develop extra topics, like the theory of orders. Prerequisites include elementary number theory and a basic familiarity with ring theory.
Author : Jean-Louis Colliot-Thélène
Publisher : Springer
Page : 251 pages
File Size : 29,61 MB
Release : 2010-10-27
Category : Mathematics
ISBN : 3642159451
Arithmetic Geometry can be defined as the part of Algebraic Geometry connected with the study of algebraic varieties through arbitrary rings, in particular through non-algebraically closed fields. It lies at the intersection between classical algebraic geometry and number theory. A C.I.M.E. Summer School devoted to arithmetic geometry was held in Cetraro, Italy in September 2007, and presented some of the most interesting new developments in arithmetic geometry. This book collects the lecture notes which were written up by the speakers. The main topics concern diophantine equations, local-global principles, diophantine approximation and its relations to Nevanlinna theory, and rationally connected varieties. The book is divided into three parts, corresponding to the courses given by J-L Colliot-Thelene, Peter Swinnerton Dyer and Paul Vojta.
