The Basic Theory Of Real Closed Spaces
DOWNLOAD
Download The Basic Theory Of Real Closed Spaces PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get The Basic Theory Of Real Closed Spaces book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
The Basic Theory Of Real Closed Spaces
DOWNLOAD
Author : Niels Schwartz
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
The Basic Theory Of Real Closed Spaces written by Niels Schwartz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
Much in the same way as classical algebraic varieties are generalized by the theory of schemes, locally semi-algebraic spaces are generalized by a class of locally ringed spaces, called real closed spaces. The underlying spaces of affine real closed spaces are real spectra of rings, the structure sheaves are called real closed sheaves. With these spaces a theory can be developed which is very similar to the theory of schemes. There is a natural functor from the category of semi-algebraic spaces to the category of real closed spaces. Via this functor properties of semi-algebraic spaces and their corresponding real closed spaces can be compared.
Real Algebraic Geometry
DOWNLOAD
Author : Michel Coste
language : en
Publisher: Springer
Release Date : 2006-11-15
Real Algebraic Geometry written by Michel Coste and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contributions by: S. Akbulut and H. King; C. Andradas and J. Ruiz; A. Borobia; L. Br|cker; G.W. Brumfield; A. Castilla; Z. Charzynski and P. Skibinski; M. Coste and M. Reguiat; A. Degtyarev; Z. Denkowska; J.-P. Francoise and F. Ronga; J.M. Gamboa and C. Ueno; D. Gondard- Cozette; I.V. Itenberg; P. Jaworski; A. Korchagin; T. Krasinksi and S. Spodzieja; K. Kurdyka; H. Lombardi; M. Marshall and L. Walter; V.F. Mazurovskii; G. Mikhalkin; T. Mostowski and E. Rannou; E.I. Shustin; N. Vorobjov.
Valuation Theory And Its Applications
DOWNLOAD
Author : Franz-Viktor Kuhlmann
language : en
Publisher: American Mathematical Soc.
Release Date : 2002-01-01
Valuation Theory And Its Applications written by Franz-Viktor Kuhlmann and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
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.
Ordered Algebraic Structures
DOWNLOAD
Author : W.C. Holland
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Ordered Algebraic Structures written by W.C. Holland and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The conference on Ordered Algebraic Structures held in Curat;ao, from the 26th of June through the 30th of June, 1995, at the Avila Beach Hotel, marked the eighth year of ac tivities by the Caribbean Mathematics Foundation (abbr. CMF), which was the principal sponsor of this conference. CMF was inaugurated in 1988 with a conference on Ordered Algebraic Structures. During the years between these two conferences the field has changed sufficiently, both from my point of view and, I believe, that of my co-organizer, W. Charles Holland, to make one wonder about the label "Ordered Algebraic Structures" itself. We recognized this from the start, and right away this conference carried a subtitle, or, if one prefers, an agenda: we concentrated on the one hand, on traditional themes in the theory of ordered groups, including model-theoretic aspects, and, on the other hand, on matters in which topology (more precisely C(X)-style topology) and category theory would play a prominent role. Plainly, ordered algebra has many faces, and it is becoming increas ingly difficult to organize an intimate conference, such as the ones encouraged in the series sponsored by CMF, in this area on a broad set of themes. These proceedings reflect, accurately we think, the spirit of the conferees, but it is not a faithful record of the papers presented at the conference.
Semi Algebraic Function Rings And Reflectors Of Partially Ordered Rings
DOWNLOAD
Author : Niels Schwartz
language : en
Publisher: Springer
Release Date : 2006-11-13
Semi Algebraic Function Rings And Reflectors Of Partially Ordered Rings written by Niels Schwartz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-13 with Mathematics categories.
The book lays algebraic foundations for real geometry through a systematic investigation of partially ordered rings of semi-algebraic functions. Real spectra serve as primary geometric objects, the maps between them are determined by rings of functions associated with the spectra. The many different possible choices for these rings of functions are studied via reflections of partially ordered rings. Readers should feel comfortable using basic algebraic and categorical concepts. As motivational background some familiarity with real geometry will be helpful. The book aims at researchers and graduate students with an interest in real algebra and geometry, ordered algebraic structures, topology and rings of continuous functions.
Constructible Sets In Real Geometry
DOWNLOAD
Author : Carlos Andradas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Constructible Sets In Real Geometry written by Carlos Andradas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book presents a systematic and unified report on the minimal description of constructible sets. It starts at a very basic level (almost undergraduate) and leads up to state-of-the-art results, many of which are published in book form for the very first time. The book contains numerous examples, 63 figures and each chapter ends with a section containing historical notes. The authors tried to keep the presentation as self-contained as it can possibly be.
Homology Of Locally Semialgebraic Spaces
DOWNLOAD
Author : Hans Delfs
language : en
Publisher: Springer
Release Date : 2006-11-14
Homology Of Locally Semialgebraic Spaces written by Hans Delfs and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Locally semialgebraic spaces serve as an appropriate framework for studying the topological properties of varieties and semialgebraic sets over a real closed field. This book contributes to the fundamental theory of semialgebraic topology and falls into two main parts. The first dealswith sheaves and their cohomology on spaces which locally look like a constructible subset of a real spectrum. Topics like families of support, homotopy, acyclic sheaves, base-change theorems and cohomological dimension are considered. In the second part a homology theory for locally complete locally semialgebraic spaces over a real closed field is developed, the semialgebraic analogue of classical Bore-Moore-homology. Topics include fundamental classes of manifolds and varieties, Poincare duality, extensions of the base field and a comparison with the classical theory. Applying semialgebraic Borel-Moore-homology, a semialgebraic ("topological") approach to intersection theory on varieties over an algebraically closed field of characteristic zero is given. The book is addressed to researchers and advanced students in real algebraic geometry and related areas.
Real And Etale Cohomology
DOWNLOAD
Author : Claus Scheiderer
language : en
Publisher: Springer
Release Date : 2006-11-15
Real And Etale Cohomology written by Claus Scheiderer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
This book makes a systematic study of the relations between the étale cohomology of a scheme and the orderings of its residue fields. A major result is that in high degrees, étale cohomology is cohomology of the real spectrum. It also contains new contributions in group cohomology and in topos theory. It is of interest to graduate students and researchers who work in algebraic geometry (not only real) and have some familiarity with the basics of étale cohomology and Grothendieck sites. Independently, it is of interest to people working in the cohomology theory of groups or in topos theory.
Faithfully Quadratic Rings
DOWNLOAD
Author : M. Dickmann
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-10-27
Faithfully Quadratic Rings written by M. Dickmann and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-27 with Mathematics categories.
In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where is not a sum of squares and is invertible. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of -isometry, where is a preorder of the given ring, , or . (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in the field case.
Manis Valuations And Pr Fer Extensions I
DOWNLOAD
Author : Manfred Knebusch
language : en
Publisher: Springer
Release Date : 2004-10-19
Manis Valuations And Pr Fer Extensions I written by Manfred Knebusch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-19 with Mathematics categories.
The present book is devoted to a study of relative Prüfer rings and Manis valuations, with an eye to application in real and p-adic geometry. If one wants to expand on the usual algebraic geometry over a non-algebraically closed base field, e.g. a real closed field or p-adically closed field, one typically meets lots of valuation domains. Usually they are not discrete and hence not noetherian. Thus, for a further develomemt of real algebraic and real analytic geometry in particular, and certainly also rigid analytic and p-adic geometry, new chapters of commutative algebra are needed, often of a non-noetherian nature. The present volume presents one such chapter.