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Author : Allen Altman
Publisher : Springer
ISBN 13 : 3540363092
Total Pages : 188 pages
Book Rating : 4.5/5 (43 download)
Download or read book Introduction to Grothendieck Duality Theory written by Allen Altman and published by Springer. This book was released on 2006-11-15 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Brian Conrad
Publisher : Springer Science & Business Media
ISBN 13 : 3540411348
Total Pages : 302 pages
Book Rating : 4.5/5 (44 download)
Download or read book Grothendieck Duality and Base Change written by Brian Conrad and published by Springer Science & Business Media. This book was released on 2000-12-12 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Grothendieck's duality theory for coherent cohomology is a fundamental tool in algebraic geometry and number theory, in areas ranging from the moduli of curves to the arithmetic theory of modular forms. Presented is a systematic overview of the entire theory, including many basic definitions and a detailed study of duality on curves, dualizing sheaves, and Grothendieck's residue symbol. Along the way proofs are given of some widely used foundational results which are not proven in existing treatments of the subject, such as the general base change compatibility of the trace map for proper Cohen-Macaulay morphisms (e.g., semistable curves). This should be of interest to mathematicians who have some familiarity with Grothendieck's work and wish to understand the details of this theory.
Author : Allen Altman
Publisher : Springer
ISBN 13 : 9783662165522
Total Pages : 192 pages
Book Rating : 4.1/5 (655 download)
Download or read book Introduction to Grothendieck Duality Theory written by Allen Altman and published by Springer. This book was released on 2014-01-15 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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Author : Allen Altman
Publisher :
ISBN 13 :
Total Pages : 184 pages
Book Rating : 4.:/5 (18 download)
Download or read book Introduction to Grothendieck Duality Theory [by] Allen Altman [and] Steven Kleiman written by Allen Altman and published by . This book was released on with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Joseph Lipman
Publisher : Springer Science & Business Media
ISBN 13 : 3540854193
Total Pages : 471 pages
Book Rating : 4.5/5 (48 download)
Download or read book Foundations of Grothendieck Duality for Diagrams of Schemes written by Joseph Lipman and published by Springer Science & Business Media. This book was released on 2009-02-05 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part written by Joseph Lipman, accessible to mid-level graduate students, is a full exposition of the abstract foundations of Grothendieck duality theory for schemes (twisted inverse image, tor-independent base change,...), in part without noetherian hypotheses, and with some refinements for maps of finite tor-dimension. The ground is prepared by a lengthy treatment of the rich formalism of relations among the derived functors, for unbounded complexes over ringed spaces, of the sheaf functors tensor, hom, direct and inverse image. Included are enhancements, for quasi-compact quasi-separated schemes, of classical results such as the projection and Künneth isomorphisms. In the second part, written independently by Mitsuyasu Hashimoto, the theory is extended to the context of diagrams of schemes. This includes, as a special case, an equivariant theory for schemes with group actions. In particular, after various basic operations on sheaves such as (derived) direct images and inverse images are set up, Grothendieck duality and flat base change for diagrams of schemes are proved. Also, dualizing complexes are studied in this context. As an application to group actions, we generalize Watanabe's theorem on the Gorenstein property of invariant subrings.
Author : Robin Hartshorne
Publisher : Lecture Notes in Mathematics
ISBN 13 :
Total Pages : 448 pages
Book Rating : 4.F/5 ( download)
Download or read book Residues and Duality written by Robin Hartshorne and published by Lecture Notes in Mathematics. This book was released on 1966 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preface.- Contents.- Introduction.- The Derived Category.- Application to Preschemes.- Duality for Projective Morphisms.- Local Cohomology.- Dualizing Complexes and Local Duality.- Residual Complexes.- The Duality Theorem.- Indices.- Bibliography
Author : David Yang Gao
Publisher : Springer Science & Business Media
ISBN 13 : 9780792361459
Total Pages : 476 pages
Book Rating : 4.3/5 (614 download)
Download or read book Duality Principles in Nonconvex Systems written by David Yang Gao and published by Springer Science & Business Media. This book was released on 2000-01-31 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.
Author : Lydia Außenhofer
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110654938
Total Pages : 392 pages
Book Rating : 4.1/5 (16 download)
Download or read book Topological Groups and the Pontryagin-van Kampen Duality written by Lydia Außenhofer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-11-22 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to topological groups and the structure theory of locally compact abelian groups, with a special emphasis on Pontryagin-van Kampen duality, including a completely self-contained elementary proof of the duality theorem. Further related topics and applications are treated in separate chapters and in the appendix.
Author : Andrei-Tudor Patrascu
Publisher : Springer
ISBN 13 : 3319461435
Total Pages : 279 pages
Book Rating : 4.3/5 (194 download)
Download or read book The Universal Coefficient Theorem and Quantum Field Theory written by Andrei-Tudor Patrascu and published by Springer. This book was released on 2016-09-23 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory. It offers a pedagogical introduction to algebraic topology, allowing readers to rapidly develop basic skills, and it also presents original ideas to inspire new research in the quest for dualities. Its ambitious goal is to construct a method based on the universal coefficient theorem for identifying new dualities connecting different domains of quantum field theory. This thesis opens a new area of research in the domain of non-perturbative physics—one in which the use of different coefficient structures in (co)homology may lead to previously unknown connections between different regimes of quantum field theories. The origin of dualities is an issue in fundamental physics that continues to puzzle the research community with unexpected results like the AdS/CFT duality or the ER-EPR conjecture. This thesis analyzes these observations from a novel and original point of view, mainly based on a fundamental connection between number theory and topology. Beyond its scientific qualities, it also offers a pedagogical introduction to advanced mathematics and its connection with physics. This makes it a valuable resource for students in mathematical physics and researchers wanting to gain insights into (co)homology theories with coefficients or the way in which Grothendieck's work may be connected with physics.
Author : Leovigildo Alonso Tarrío
Publisher : American Mathematical Soc.
ISBN 13 : 0821819429
Total Pages : 138 pages
Book Rating : 4.8/5 (218 download)
Download or read book Studies in Duality on Noetherian Formal Schemes and Non-Noetherian Ordinary Schemes written by Leovigildo Alonso Tarrío and published by American Mathematical Soc.. This book was released on 1999 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains three papers on the foundations of Grothendieck duality on Noetherian formal schemes and on not-necessarily-Noetherian ordinary schemes. The first paper presents a self-contained treatment for formal schemes which synthesizes several duality-related topics, such as local duality, formal duality, residue theorems, dualizing complexes, etc. Included is an exposition of properties of torsion sheaves and of limits of coherent sheaves. A second paper extends Greenlees-May duality to complexes on formal schemes. This theorem has important applications to Grothendieck duality. The third paper outlines methods for eliminating the Noetherian hypotheses. A basic role is played by Kiehl's theorem affirming conservation of pseudo-coherence of complexes under proper pseudo-coherent maps. This work gives a detailed introduction to the subject of Grothendieck Duality. The approach is unique in its presentation of a complex series of special cases that build up to the main results.
Author : J. S. Milne
Publisher :
ISBN 13 :
Total Pages : 440 pages
Book Rating : 4.3/5 (97 download)
Download or read book Arithmetic Duality Theorems written by J. S. Milne and published by . This book was released on 1986 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here, published for the first time, are the complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry. The text covers these theorems in Galois cohomology, ,tale cohomology, and flat cohomology and addresses applications in the above areas. The writing is expository and the book will serve as an invaluable reference text as well as an excellent introduction to the subject.
Author : Graham Clenaghan
Publisher :
ISBN 13 :
Total Pages : 45 pages
Book Rating : 4.:/5 (947 download)
Download or read book Grothendieck Duality on Diagrams of Schemes written by Graham Clenaghan and published by . This book was released on 2015 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Du Bois complex and Du Bois singularities, which extend results of Hodge theory to singular complex varieties, can be defined in terms of a cubical hyperresolution. In this dissertation I further develop the language of diagrams of schemes and then prove analogues of Grothendieck duality and other cohomological theorems for cubical diagrams. I then demonstrate the use of these by revisiting some known results about the Du Bois complex from a different perspective, and proving new results concerning the cohomology of a contraction.
Author : Emily Riehl
Publisher : Courier Dover Publications
ISBN 13 : 0486820807
Total Pages : 273 pages
Book Rating : 4.4/5 (868 download)
Download or read book Category Theory in Context written by Emily Riehl and published by Courier Dover Publications. This book was released on 2017-03-09 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.
Author : Brian Conrad
Publisher : Springer
ISBN 13 : 354040015X
Total Pages : 302 pages
Book Rating : 4.5/5 (44 download)
Download or read book Grothendieck Duality and Base Change written by Brian Conrad and published by Springer. This book was released on 2003-07-01 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Grothendieck's duality theory for coherent cohomology is a fundamental tool in algebraic geometry and number theory, in areas ranging from the moduli of curves to the arithmetic theory of modular forms. Presented is a systematic overview of the entire theory, including many basic definitions and a detailed study of duality on curves, dualizing sheaves, and Grothendieck's residue symbol. Along the way proofs are given of some widely used foundational results which are not proven in existing treatments of the subject, such as the general base change compatibility of the trace map for proper Cohen-Macaulay morphisms (e.g., semistable curves). This should be of interest to mathematicians who have some familiarity with Grothendieck's work and wish to understand the details of this theory.
Author : Lou Van den Dries
Publisher : Cambridge University Press
ISBN 13 : 0521598389
Total Pages : 196 pages
Book Rating : 4.5/5 (215 download)
Download or read book Tame Topology and O-minimal Structures written by Lou Van den Dries and published by Cambridge University Press. This book was released on 1998-05-07 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes give a self-contained treatment of the theory of o-minimal structures from a geometric and topological viewpoint, assuming only rudimentary algebra and analysis. This book should be of interest to model theorists, analytic geometers and topologists.
Author : Barbara Fantechi
Publisher : American Mathematical Soc.
ISBN 13 : 0821842455
Total Pages : 354 pages
Book Rating : 4.8/5 (218 download)
Download or read book Fundamental Algebraic Geometry written by Barbara Fantechi and published by American Mathematical Soc.. This book was released on 2005 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an outline of Alexander Grothendieck's theories. This book discusses four main themes - descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. It is suitable for those working in algebraic geometry.
Author : Richard Hartshorne
Publisher :
ISBN 13 : 9780387036038
Total Pages : pages
Book Rating : 4.0/5 (36 download)
Download or read book Residues and Duality written by Richard Hartshorne and published by . This book was released on 1966-01-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
