Kategoria BISAC: Mathematics >> Geometry - Algebraic

" The first] ten chapters...are an efficient, accessible, and self-contained introduction to affine algebraic groups over an algebraically closed field. The author includes exercises and the book is certainly usable by graduate students as a text or for self-study...the author has a] student-friendly style The following] seven chapters... would also be a good introduction to rationality issues for algebraic groups. A number of results from the literature appear for the first time in a text."

Mathematical Reviews (Review of the Second...

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...

The authors develop thorough and complete foundations for the method of almost etale extensions, which is at the basis of Faltings' approach to p-adic Hodge theory. The central notion is that of an "almost ring." Almost rings are the commutative unitary monoids in a tensor category obtained as a quotient V-Mod/S of the category V-Mod of modules over a fixed ring V; the subcategory S consists of all modules annihilated by a fixed ideal m of V, satisfying certain natural conditions.

The reader is assumed to be familiar with general categorical notions, some basic commutative algebra...

In this book, the author writes freely and often humorously about his life, beginning with his earliest childhood days. He describes his survival of American bombing raids when he was a teenager in Japan, his emergence as a researcher in a post-war university system that was seriously deficient, and his life as a mature mathematician in Princeton and in the international academic community. Every page of this memoir contains personal observations and striking stories. Such luminaries as Chevalley, Oppenheimer, Siegel, and Weil figure prominently in its anecdotes.

Goro Shimura...

Formes sesquilineaires et formes quadratiques

Les Elements de mathematique de Nicolas BOURBAKI ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements.

Ce neuvieme chapitre du Livre d'Algebre, deuxieme Livre du traite, est consacre aux formes quadratiques, symplectiques ou hermitiennes et aux groupes associes.

Il contient egalement une note historique.

Ce volume est une reimpression de l'edition de 1959.

Ce livre contient une demonstration detaillee et complete de l'existence d'un isomorphisme equivariant entre les tours p-adiques de Lubin-Tate et de Drinfeld. Le resultat est etabli en egales et inegales caracteristiques. Il y est egalement donne comme application une demonstration du fait que les cohomologies equivariantes de ces deux tours sont isomorphes, un resultat qui a des applications a l'etude de la correspondance de Langlands locale. Au cours de la preuve des rappels et des complements sont donnes sur la structure des deux espaces de modules precedents, les groupes formels...

Integral Closure gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. These are shared concerns in commutative algebra, algebraic geometry, number theory and the computational aspects of these fields. The overall goal is to determine and analyze the equations of the assemblages of the set of solutions that arise under various processes and algorithms. It gives a comprehensive treatment of Rees algebras and multiplicity theory - while pointing to applications in many other problem areas. Its main goal is to provide complexity...

Cet ouvrage est consacre a l'arithmetique des surfaces fibrees en courbes de genre 1 au-dessus de la droite projective, et a l'arithmetique des intersections de deux quadriques dans l'espace projectif. Swinnerton-Dyer introduisit en 1993 une technique permettant d'etudier les points rationnels des pinceaux de courbes de genre 1. La premiere moitie de l'ouvrage reprend et developpe cette technique ainsi que ses generalisations ulterieures. La seconde moitie, qui repose sur la premiere, porte sur les surfaces de del Pezzo de degre 4 et sur les intersections de deux quadriques de dimension...

Multiplicative invariant theory, as a research area in its own right within the wider spectrum of invariant theory, is of relatively recent vintage. The present text offers a coherent account of the basic results achieved thus far..

Multiplicative invariant theory is intimately tied to integral representations of finite groups. Therefore, the field has a predominantly discrete, algebraic flavor. Geometry, specifically the theory of algebraic groups, enters through Weyl groups and their root lattices as well as via character lattices of algebraic tori.

Throughout the text,...