Traces Of Differential Forms And Hochschild Homology

Author : Reinhold Hübl
Publisher : Springer
Page : 115 pages
File Size : 44,7 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540461258

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Traces of Differential Forms and Hochschild Homology by Reinhold Hübl Pdf

This monograph provides an introduction to, as well as a unification and extension of the published work and some unpublished ideas of J. Lipman and E. Kunz about traces of differential forms and their relations to duality theory for projective morphisms. The approach uses Hochschild-homology, the definition of which is extended to the category of topological algebras. Many results for Hochschild-homology of commutative algebras also hold for Hochschild-homology of topological algebras. In particular, after introducing an appropriate notion of completion of differential algebras, one gets a natural transformation between differential forms and Hochschild-homology of topological algebras. Traces of differential forms are of interest to everyone working with duality theory and residue symbols. Hochschild-homology is a useful tool in many areas of k-theory. The treatment is fairly elementary and requires only little knowledge in commutative algebra and algebraic geometry.

Author : Joseph Lipman
Publisher : American Mathematical Soc.
Page : 95 pages
File Size : 55,9 Mb
Release : 1987
Category : Mathematics
ISBN : 9780821850701

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Residues and Traces of Differential Forms Via Hochschild Homology by Joseph Lipman Pdf

Requiring only some understanding of homological algebra and commutative ring theory, this book will give those who have encountered Grothendieck residues in geometry or complex analysis a better understanding of residues, as well as an appreciation of Hochschild homology. While numerous papers have treated the topic of residues from a variety of viewpoints, no books have addressed this topic. The author fills this gap by using Hochschild homology to provide a natural, general, and easily accessible approach to residues, and by identifying connections with other treatments of residues. Developing a theory of the Grothendieck symbol by means of elementary homological and commutative algebra, the author derives residues from a simple pairing between Hochschild homology and cohomology groups, and defines all concepts along the way. The author also establishes some functorial properties and introduces certain trace and cotrace maps with potential use in other contexts.

Author : Reinhold Hubl
Publisher : Unknown
Page : 124 pages
File Size : 43,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662198614

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Traces of Differential Forms and Hochschild Homology by Reinhold Hubl Pdf

Author : Gennady Lybeznik
Publisher : CRC Press
Page : 358 pages
File Size : 46,6 Mb
Release : 2001-10-18
Category : Mathematics
ISBN : 9781482275766

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Local Cohomology and Its Applications by Gennady Lybeznik Pdf

This volume collects presentations from the international workshop on local cohomology held in Guanajuato, Mexico, including expanded lecture notes of two minicourses on applications in equivariant topology and foundations of duality theory, and chapters on finiteness properties, D-modules, monomial ideals, combinatorial analysis, and related topics. Featuring selected papers from renowned experts around the world, Local Cohomology and Its Applications is a provocative reference for algebraists, topologists, and upper-level undergraduate and graduate students in these disciplines.

Author : Ernst Kunz,Rolf Waldi
Publisher : American Mathematical Soc.
Page : 153 pages
File Size : 49,8 Mb
Release : 1988
Category : Mathematics
ISBN : 9780821850855

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Regular Differential Forms by Ernst Kunz,Rolf Waldi Pdf

This book is aimed at students and researchers in commutative algebra, algebraic geometry, and neighboring disciplines. The book will provide readers with new insight into differential forms and may stimulate new research through the many open questions it raises. The authors introduce various sheaves of differential forms for equidimensional morphisms of finite type between noetherian schemes, the most important being the sheaf of regular differential forms. It is known in many cases that the top degree regular differentials form a dualizing sheaf in the sense of duality theory. All constructions in the book are purely local and require only prerequisites from the theory of commutative noetherian rings and their Kahler differentials. The authors study the relations between the sheaves under consideration and give some applications to local properties of morphisms.The investigation of the 'fundamental class', a canonical homomorphism from Kahler to regular differential forms, is a major topic. The book closes with applications to curve singularities. While regular differential forms have been previously studied mainly in the 'absolute case' (that is, for algebraic varieties over fields), this book deals with the relative situation. Moreover, the authors strive to avoid 'separability assumptions'. Once the construction of regular differential forms is given, many results can be transferred from the absolute to the relative case.

Author : Thorsten Holm,Peter Jørgensen,Raphaël Rouquier
Publisher : Cambridge University Press
Page : 473 pages
File Size : 49,8 Mb
Release : 2010-06-24
Category : Mathematics
ISBN : 9781139488884

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Triangulated Categories by Thorsten Holm,Peter Jørgensen,Raphaël Rouquier Pdf

A 2010 collection of survey articles by leading experts covering fundamental aspects of triangulated categories, as well as applications in algebraic geometry, representation theory, commutative algebra, microlocal analysis and algebraic topology. This is a valuable reference for experts and a useful introduction for graduate students entering the field.

Author : Cristodor Ionescu
Publisher : Springer Nature
Page : 487 pages
File Size : 42,9 Mb
Release : 2023-03-28
Category : Mathematics
ISBN : 9783031222924

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Classes of Good Noetherian Rings by Cristodor Ionescu Pdf

This monograph provides an exhaustive treatment of several classes of Noetherian rings and morphisms of Noetherian local rings. Chapters carefully examine some of the most important topics in the area, including Nagata, F-finite and excellent rings, Bertini’s Theorem, and Cohen factorizations. Of particular interest is the presentation of Popescu’s Theorem on Neron Desingularization and the structure of regular morphisms, with a complete proof. Classes of Good Noetherian Rings will be an invaluable resource for researchers in commutative algebra, algebraic and arithmetic geometry, and number theory.

Author : Steven Lord,Edward McDonald,Fedor Sukochev,Dmitriy Zanin
Publisher : Walter de Gruyter GmbH & Co KG
Page : 4197 pages
File Size : 47,7 Mb
Release : 2023-04-03
Category : Mathematics
ISBN : 9783110700244

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Trace Formulas by Steven Lord,Edward McDonald,Fedor Sukochev,Dmitriy Zanin Pdf

This volume introduces noncommutative integration theory on semifinite von Neumann algebras and the theory of singular traces for symmetric operator spaces. Deeper aspects of the association between measurability, poles and residues of spectral zeta functions, and asymptotics of heat traces are studied. Applications in Connes’ noncommutative geometry that are detailed include integration of quantum differentials, measures on fractals, and Connes’ character formula concerning the Hochschild class of the Chern character.

Author : Jean-Louis Loday
Publisher : Springer Science & Business Media
Page : 467 pages
File Size : 54,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662217399

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Cyclic Homology by Jean-Louis Loday Pdf

This book is a comprehensive study of cyclic homology theory together with its relationship with Hochschild homology, de Rham cohomology, S1 equivariant homology, the Chern character, Lie algebra homology, algebraic K-theory and non-commutative differential geometry. Though conceived as a basic reference on the subject, many parts of this book are accessible to graduate students.

Author : Ernst Kunz
Publisher : American Mathematical Soc.
Page : 177 pages
File Size : 41,5 Mb
Release : 2008
Category : Algebraic varieties
ISBN : 9780821847602

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Residues and Duality for Projective Algebraic Varieties by Ernst Kunz Pdf

"This book, which grew out of lectures by E. Kunz for students with a background in algebra and algebraic geometry, develops local and global duality theory in the special case of (possibly singular) algebraic varieties over algebraically closed base fields. It describes duality and residue theorems in terms of Kahler differential forms and their residues. The properties of residues are introduced via local cohomology. Special emphasis is given to the relation between residues to classical results of algebraic geometry and their generalizations." "The contribution by A. Dickenstein gives applications of residues and duality to polynomial solutions of constant coefficient partial differential equations and to problems in interpolation and ideal membership, D. A. Cox explains toric residues and relates them to the earlier text." "The book is intended as an introduction to more advanced treatments and further applications of the subject, to which numerous bibliographical hints are given."--BOOK JACKET.

Author : Guillermo Cortiñas,Charles A. Weibel
Publisher : American Mathematical Soc.
Page : 388 pages
File Size : 46,7 Mb
Release : 2024-06-29
Category : Education
ISBN : 9781470450267

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K-theory in Algebra, Analysis and Topology by Guillermo Cortiñas,Charles A. Weibel Pdf

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.

Author : Leovigildo Alonso Tarrío,Leovigildo Alonso,Ana Jeremías López,Joseph Lipman
Publisher : American Mathematical Soc.
Page : 138 pages
File Size : 50,6 Mb
Release : 1999
Category : Duality theory (Mathematics).
ISBN : 9780821819425

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Studies in Duality on Noetherian Formal Schemes and Non-Noetherian Ordinary Schemes by Leovigildo Alonso Tarrío,Leovigildo Alonso,Ana Jeremías López,Joseph Lipman Pdf

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 : Dale Husemöller
Publisher : Unknown
Page : 134 pages
File Size : 53,8 Mb
Release : 1991
Category : Algebra, Homological
ISBN : UCSD:31822015022072

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Lectures on Cyclic Homology by Dale Husemöller Pdf

Author : Ali Chamseddine,Caterina Consani,Nigel Higson,Masoud Khalkhali,Henri Moscovici,Guoliang Yu
Publisher : Springer Nature
Page : 753 pages
File Size : 48,9 Mb
Release : 2020-01-13
Category : Mathematics
ISBN : 9783030295974

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Advances in Noncommutative Geometry by Ali Chamseddine,Caterina Consani,Nigel Higson,Masoud Khalkhali,Henri Moscovici,Guoliang Yu Pdf

This authoritative volume in honor of Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject. The book features an amalgam of invited survey and research papers that will no doubt be accessed, read, and referred to, for several decades to come. The pertinence and potency of new concepts and methods are concretely illustrated in each contribution. Much of the content is a direct outgrowth of the Noncommutative Geometry conference, held March 23–April 7, 2017, in Shanghai, China. The conference covered the latest research and future areas of potential exploration surrounding topology and physics, number theory, as well as index theory and its ramifications in geometry.

Author : Hieronymus Georg Zeuthen,Steven L. Kleiman,Anders Thorup
Publisher : American Mathematical Soc.
Page : 278 pages
File Size : 46,8 Mb
Release : 1991
Category : Mathematics
ISBN : 9780821851319

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Enumerative Algebraic Geometry by Hieronymus Georg Zeuthen,Steven L. Kleiman,Anders Thorup Pdf

1989 marked the 150th anniversary of the birth of the great Danish mathematician Hieronymus Georg Zeuthen. Zeuthen's name is known to every algebraic geometer because of his discovery of a basic invariant of surfaces. However, he also did fundamental research in intersection theory, enumerative geometry, and the projective geometry of curves and surfaces. Zeuthen's extraordinary devotion to his subject, his characteristic depth, thoroughness, and clarity of thought, and his precise and succinct writing style are truly inspiring. During the past ten years or so, algebraic geometers have reexamined Zeuthen's work, drawing from it inspiration and new directions for development in the field. The 1989 Zeuthen Symposium, held in the summer of 1989 at the Mathematical Institute of the University of Copenhagen, provided a historic opportunity for mathematicians to gather and examine those areas in contemporary mathematical research which have evolved from Zeuthen's fruitful ideas. This volume, containing papers presented during the symposium, as well as others inspired by it, illuminates some currently active areas of research in enumerative algebraic geometry.