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Author : Yoon Sung Hwang
Publisher : Unknown
Page : 270 pages
File Size : 41,7 Mb
Release : 1992
Category : Electronic
ISBN : UCSD:31822005087903
Author : Franz-Viktor Kuhlmann,Salma Kuhlmann,Murray Marshall
Publisher : American Mathematical Soc.
Page : 470 pages
File Size : 50,6 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 0821871390
This book is the first of two proceedings volumes stemming from the International Conference and Workshop on Valuation Theory held at the University of Saskatchewan (Saskatoon, SK, Canada). Valuation theory arose in the early part of the twentieth century in connection with number theory and has many important applications to geometry and analysis: the classical application to the study of algebraic curves and to Dedekind and Prufer domains; the close connection to the famousresolution of the singularities problem; the study of the absolute Galois group of a field; the connection between ordering, valuations, and quadratic forms over a formally real field; the application to real algebraic geometry; the study of noncommutative rings; etc. The special feature of this book isits focus on current applications of valuation theory to this broad range of topics. Also included is a paper on the history of valuation theory. The book is suitable for graduate students and research mathematicians working in algebra, algebraic geometry, number theory, and mathematical logic.
Author : Anonim
Publisher : Unknown
Page : 608 pages
File Size : 46,6 Mb
Release : 1995
Category : Mathematics
ISBN : UCAL:B4334179
Author : Frank Hung-Yueh Chang
Publisher : Unknown
Page : 276 pages
File Size : 40,8 Mb
Release : 2004
Category : Electronic
ISBN : UCSD:31822009434630
Author : H. Marubayashi,Haruo Miyamoto,Akira Ueda
Publisher : Springer Science & Business Media
Page : 201 pages
File Size : 53,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401724364
Much progress has been made during the last decade on the subjects of non commutative valuation rings, and of semi-hereditary and Priifer orders in a simple Artinian ring which are considered, in a sense, as global theories of non-commu tative valuation rings. So it is worth to present a survey of the subjects in a self-contained way, which is the purpose of this book. Historically non-commutative valuation rings of division rings were first treat ed systematically in Schilling's Book [Sc], which are nowadays called invariant valuation rings, though invariant valuation rings can be traced back to Hasse's work in [Has]. Since then, various attempts have been made to study the ideal theory of orders in finite dimensional algebras over fields and to describe the Brauer groups of fields by usage of "valuations", "places", "preplaces", "value functions" and "pseudoplaces". In 1984, N. 1. Dubrovin defined non-commutative valuation rings of simple Artinian rings with notion of places in the category of simple Artinian rings and obtained significant results on non-commutative valuation rings (named Dubrovin valuation rings after him) which signify that these rings may be the correct def inition of valuation rings of simple Artinian rings. Dubrovin valuation rings of central simple algebras over fields are, however, not necessarily to be integral over their centers.
Author : Anonim
Publisher : Unknown
Page : 516 pages
File Size : 44,9 Mb
Release : 1997
Category : Mathematics
ISBN : UOM:39015049401022
Author : Anonim
Publisher : Unknown
Page : 692 pages
File Size : 52,9 Mb
Release : 2004
Category : Dissertations, Academic
ISBN : STANFORD:36105114637387
Author : Anonim
Publisher : Unknown
Page : 1100 pages
File Size : 53,9 Mb
Release : 2001
Category : Mathematics
ISBN : UVA:X006170285
Author : American Mathematical Society
Publisher : Unknown
Page : 852 pages
File Size : 55,8 Mb
Release : 1992
Category : Mathematics
ISBN : UCSD:31822015782311
Author : John Dauns
Publisher : Unknown
Page : 446 pages
File Size : 46,8 Mb
Release : 1982
Category : Mathematics
ISBN : UOM:39015042079296
Author : Anonim
Publisher : Unknown
Page : 796 pages
File Size : 46,6 Mb
Release : 1992
Category : Dissertation abstracts
ISBN : UOM:39015086908244
Author : Jean-Louis Colliot-Thélène,Alexei N. Skorobogatov
Publisher : Springer Nature
Page : 450 pages
File Size : 46,8 Mb
Release : 2021-07-30
Category : Mathematics
ISBN : 9783030742485
This monograph provides a systematic treatment of the Brauer group of schemes, from the foundational work of Grothendieck to recent applications in arithmetic and algebraic geometry. The importance of the cohomological Brauer group for applications to Diophantine equations and algebraic geometry was discovered soon after this group was introduced by Grothendieck. The Brauer–Manin obstruction plays a crucial role in the study of rational points on varieties over global fields. The birational invariance of the Brauer group was recently used in a novel way to establish the irrationality of many new classes of algebraic varieties. The book covers the vast theory underpinning these and other applications. Intended as an introduction to cohomological methods in algebraic geometry, most of the book is accessible to readers with a knowledge of algebra, algebraic geometry and algebraic number theory at graduate level. Much of the more advanced material is not readily available in book form elsewhere; notably, de Jong’s proof of Gabber’s theorem, the specialisation method and applications of the Brauer group to rationality questions, an in-depth study of the Brauer–Manin obstruction, and proof of the finiteness theorem for the Brauer group of abelian varieties and K3 surfaces over finitely generated fields. The book surveys recent work but also gives detailed proofs of basic theorems, maintaining a balance between general theory and concrete examples. Over half a century after Grothendieck's foundational seminars on the topic, The Brauer–Grothendieck Group is a treatise that fills a longstanding gap in the literature, providing researchers, including research students, with a valuable reference on a central object of algebraic and arithmetic geometry.
Author : Abraham Adrian Albert
Publisher : American Mathematical Soc.
Page : 224 pages
File Size : 42,6 Mb
Release : 1939-12-31
Category : Mathematics
ISBN : 9780821810248
The first three chapters of this work contain an exposition of the Wedderburn structure theorems. Chapter IV contains the theory of the commutator subalgebra of a simple subalgebra of a normal simple algebra, the study of automorphisms of a simple algebra, splitting fields, and the index reduction factor theory. The fifth chapter contains the foundation of the theory of crossed products and of their special case, cyclic algebras. The theory of exponents is derived there as well as the consequent factorization of normal division algebras into direct factors of prime-power degree. Chapter VI consists of the study of the abelian group of cyclic systems which is applied in Chapter VII to yield the theory of the structure of direct products of cyclic algebras and the consequent properties of norms in cyclic fields. This chapter is closed with the theory of $p$-algebras. In Chapter VIII an exposition is given of the theory of the representations of algebras. The treatment is somewhat novel in that while the recent expositions have used representation theorems to obtain a number of results on algebras, here the theorems on algebras are themselves used in the derivation of results on representations. The presentation has its inspiration in the author's work on the theory of Riemann matrices and is concluded by the introduction to the generalization (by H. Weyl and the author) of that theory. The theory of involutorial simple algebras is derived in Chapter X both for algebras over general fields and over the rational field. The results are also applied in the determination of the structure of the multiplication algebras of all generalized Riemann matrices, a result which is seen in Chapter XI to imply a complete solution of the principal problem on Riemann matrices.
Author : Bjorn Poonen
Publisher : American Mathematical Society
Page : 357 pages
File Size : 52,6 Mb
Release : 2023-08-10
Category : Mathematics
ISBN : 9781470474584
This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one—this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and descent obstructions. A final chapter applies all these to study the arithmetic of surfaces. The down-to-earth explanations and the over 100 exercises make the book suitable for use as a graduate-level textbook, but even experts will appreciate having a single source covering many aspects of geometry over an unrestricted ground field and containing some material that cannot be found elsewhere. The origins of arithmetic (or Diophantine) geometry can be traced back to antiquity, and it remains a lively and wide research domain up to our days. The book by Bjorn Poonen, a leading expert in the field, opens doors to this vast field for many readers with different experiences and backgrounds. It leads through various algebraic geometric constructions towards its central subject: obstructions to existence of rational points. —Yuri Manin, Max-Planck-Institute, Bonn It is clear that my mathematical life would have been very different if a book like this had been around at the time I was a student. —Hendrik Lenstra, University Leiden Understanding rational points on arbitrary algebraic varieties is the ultimate challenge. We have conjectures but few results. Poonen's book, with its mixture of basic constructions and openings into current research, will attract new generations to the Queen of Mathematics. —Jean-Louis Colliot-Thélène, Université Paris-Sud A beautiful subject, handled by a master. —Joseph Silverman, Brown University
Author : Jean-Pierre Serre
Publisher : CRC Press
Page : 120 pages
File Size : 50,6 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781439865255
This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the first part of the book, classical methods and results, such as the Scholz and Reichardt constructi