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Foundations Of Grothendieck Duality For Diagrams Of Schemes
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Book Synopsis Foundations of Grothendieck Duality for Diagrams of Schemes by : Joseph Lipman
Download or read book Foundations of Grothendieck Duality for Diagrams of Schemes written by Joseph Lipman and published by Springer. This book was released on 2009-03-07 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part One of this book covers the abstract foundations of Grothendieck duality theory for schemes in part with noetherian hypotheses and with some refinements for maps of finite tor-dimension. Part Two extends the theory to the context of diagrams of schemes.
Book Synopsis Foundations of Grothendieck Duality for Diagrams of Schemes by : Joseph Lipman
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.
Book Synopsis Introduction to Grothendieck Duality Theory by : Allen Altman
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:
Book Synopsis Studies in Duality on Noetherian Formal Schemes and Non-Noetherian Ordinary Schemes by : Leovigildo Alonso Tarrío
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.
Book Synopsis K-theory in Algebra, Analysis and Topology by : Guillermo Cortiñas
Download or read book K-theory in Algebra, Analysis and Topology written by Guillermo Cortiñas and published by American Mathematical Soc.. This book was released on with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the ICM 2018 satellite school and workshop K-theory conference in Argentina. The school was held from July 16–20, 2018, in La Plata, Argentina, and the workshop was held from July 23–27, 2018, in Buenos Aires, Argentina. The volume showcases current developments in K-theory and related areas, including motives, homological algebra, index theory, operator algebras, and their applications and connections. Papers cover topics such as K-theory of group rings, Witt groups of real algebraic varieties, coarse homology theories, topological cyclic homology, negative K-groups of monoid algebras, Milnor K-theory and regulators, noncommutative motives, the classification of C∗-algebras via Kasparov's K-theory, the comparison between full and reduced C∗-crossed products, and a proof of Bott periodicity using almost commuting matrices.
Book Synopsis Algebraic Geometry II: Cohomology of Schemes by : Ulrich Görtz
Download or read book Algebraic Geometry II: Cohomology of Schemes written by Ulrich Görtz and published by Springer Nature. This book was released on 2023-11-22 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book completes the comprehensive introduction to modern algebraic geometry which was started with the introductory volume Algebraic Geometry I: Schemes. It begins by discussing in detail the notions of smooth, unramified and étale morphisms including the étale fundamental group. The main part is dedicated to the cohomology of quasi-coherent sheaves. The treatment is based on the formalism of derived categories which allows an efficient and conceptual treatment of the theory, which is of crucial importance in all areas of algebraic geometry. After the foundations are set up, several more advanced topics are studied, such as numerical intersection theory, an abstract version of the Theorem of Grothendieck-Riemann-Roch, the Theorem on Formal Functions, Grothendieck's algebraization results and a very general version of Grothendieck duality. The book concludes with chapters on curves and on abelian schemes, which serve to develop the basics of the theory of these two important classes of schemes on an advanced level, and at the same time to illustrate the power of the techniques introduced previously. The text contains many exercises that allow the reader to check their comprehension of the text, present further examples or give an outlook on further results.
Book Synopsis Commutative Algebra and Noncommutative Algebraic Geometry by : David Eisenbud
Download or read book Commutative Algebra and Noncommutative Algebraic Geometry written by David Eisenbud and published by Cambridge University Press. This book was released on 2015-11-19 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys fundamental current topics in these two areas of research, emphasising the lively interaction between them. Volume 1 contains expository papers ideal for those entering the field.
Book Synopsis Derived Categories by : Amnon Yekutieli
Download or read book Derived Categories written by Amnon Yekutieli and published by Cambridge University Press. This book was released on 2019-12-19 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first systematic exposition of the theory of derived categories, with key applications in commutative and noncommutative algebra.
Book Synopsis Bousfield Classes and Ohkawa's Theorem by : Takeo Ohsawa
Download or read book Bousfield Classes and Ohkawa's Theorem written by Takeo Ohsawa and published by Springer Nature. This book was released on 2020-03-18 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume originated in the workshop held at Nagoya University, August 28–30, 2015, focusing on the surprising and mysterious Ohkawa's theorem: the Bousfield classes in the stable homotopy category SH form a set. An inspiring, extensive mathematical story can be narrated starting with Ohkawa's theorem, evolving naturally with a chain of motivational questions: Ohkawa's theorem states that the Bousfield classes of the stable homotopy category SH surprisingly forms a set, which is still very mysterious. Are there any toy models where analogous Bousfield classes form a set with a clear meaning? The fundamental theorem of Hopkins, Neeman, Thomason, and others states that the analogue of the Bousfield classes in the derived category of quasi-coherent sheaves Dqc(X) form a set with a clear algebro-geometric description. However, Hopkins was actually motivated not by Ohkawa's theorem but by his own theorem with Smith in the triangulated subcategory SHc, consisting of compact objects in SH. Now the following questions naturally occur: (1) Having theorems of Ohkawa and Hopkins-Smith in SH, are there analogues for the Morel-Voevodsky A1-stable homotopy category SH(k), which subsumes SH when k is a subfield of C?, (2) Was it not natural for Hopkins to have considered Dqc(X)c instead of Dqc(X)? However, whereas there is a conceptually simple algebro-geometrical interpretation Dqc(X)c = Dperf(X), it is its close relative Dbcoh(X) that traditionally, ever since Oka and Cartan, has been intensively studied because of its rich geometric and physical information. This book contains developments for the rest of the story and much more, including the chromatics homotopy theory, which the Hopkins–Smith theorem is based upon, and applications of Lurie's higher algebra, all by distinguished contributors.
Book Synopsis Rationality Problems in Algebraic Geometry by : Arnaud Beauville
Download or read book Rationality Problems in Algebraic Geometry written by Arnaud Beauville and published by Springer. This book was released on 2016-12-06 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It offers a comprehensive introduction to this fascinating topic, and will certainly become an essential reference for anybody working in the field. Rationality problems are of fundamental importance both in algebra and algebraic geometry. Historically, rationality problems motivated significant developments in the theory of abelian integrals, Riemann surfaces and the Abel–Jacobi map, among other areas, and they have strong links with modern notions such as moduli spaces, Hodge theory, algebraic cycles and derived categories. This text is aimed at researchers and graduate students in algebraic geometry.
Book Synopsis Completion, Čech and Local Homology and Cohomology by : Peter Schenzel
Download or read book Completion, Čech and Local Homology and Cohomology written by Peter Schenzel and published by Springer. This book was released on 2018-09-15 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the present monograph is a thorough study of the adic-completion, its left derived functors and their relations to the local cohomology functors, as well as several completeness criteria, related questions and various dualities formulas. A basic construction is the Čech complex with respect to a system of elements and its free resolution. The study of its homology and cohomology will play a crucial role in order to understand left derived functors of completion and right derived functors of torsion. This is useful for the extension and refinement of results known for modules to unbounded complexes in the more general setting of not necessarily Noetherian rings. The book is divided into three parts. The first one is devoted to modules, where the adic-completion functor is presented in full details with generalizations of some previous completeness criteria for modules. Part II is devoted to the study of complexes. Part III is mainly concerned with duality, starting with those between completion and torsion and leading to new aspects of various dualizing complexes. The Appendix covers various additional and complementary aspects of the previous investigations and also provides examples showing the necessity of the assumptions. The book is directed to readers interested in recent progress in Homological and Commutative Algebra. Necessary prerequisites include some knowledge of Commutative Algebra and a familiarity with basic Homological Algebra. The book could be used as base for seminars with graduate students interested in Homological Algebra with a view towards recent research.
Book Synopsis Topology of Stratified Spaces by : Greg Friedman
Download or read book Topology of Stratified Spaces written by Greg Friedman and published by Cambridge University Press. This book was released on 2011-03-28 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the study of singular spaces using techniques from areas within geometry and topology and the interactions among them.
Book Synopsis Commutative Algebra by : Irena Peeva
Download or read book Commutative Algebra written by Irena Peeva and published by Springer Science & Business Media. This book was released on 2013-02-01 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, including core areas in Commutative Algebra and also relations to Algebraic Geometry, Algebraic Combinatorics, Hyperplane Arrangements, Homological Algebra, and String Theory. The book aims to showcase the area, especially for the benefit of junior mathematicians and researchers who are new to the field; it will aid them in broadening their background and to gain a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research.
Book Synopsis A Gentle Introduction to Homological Mirror Symmetry by : Raf Bocklandt
Download or read book A Gentle Introduction to Homological Mirror Symmetry written by Raf Bocklandt and published by Cambridge University Press. This book was released on 2021-08-19 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homological mirror symmetry has its origins in theoretical physics but is now of great interest in mathematics due to the deep connections it reveals between different areas of geometry and algebra. This book offers a self-contained and accessible introduction to the subject via the representation theory of algebras and quivers. It is suitable for graduate students and others without a great deal of background in homological algebra and modern geometry. Each part offers a different perspective on homological mirror symmetry. Part I introduces the A-infinity formalism and offers a glimpse of mirror symmetry using representations of quivers. Part II discusses various A- and B-models in mirror symmetry and their connections through toric and tropical geometry. Part III deals with mirror symmetry for Riemann surfaces. The main mathematical ideas are illustrated by means of simple examples coming mainly from the theory of surfaces, helping the reader connect theory with intuition.
Book Synopsis Introduction to Complex Reflection Groups and Their Braid Groups by : Michel Broué
Download or read book Introduction to Complex Reflection Groups and Their Braid Groups written by Michel Broué and published by Springer. This book was released on 2010-01-28 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers basic properties of complex reflection groups, such as characterization, Steinberg theorem, Gutkin-Opdam matrices, Solomon theorem and applications, including the basic findings of Springer theory on eigenspaces.
Book Synopsis Introduction to Grothendieck Duality Theory by : Allen Altman
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:
Book Synopsis The Dirac Spectrum by : Nicolas Ginoux
Download or read book The Dirac Spectrum written by Nicolas Ginoux and published by Springer. This book was released on 2009-05-30 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume surveys the spectral properties of the spin Dirac operator. After a brief introduction to spin geometry, it presents the main known estimates for Dirac eigenvalues on compact manifolds with or without boundaries.
