Studies In Duality On Noetherian Formal Schemes And Non Noetherian Ordinary Schemes

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Studies in Duality on Noetherian Formal Schemes and Non-Noetherian Ordinary Schemes

Leovigildo Alonso Tarrío,Leovigildo Alonso,Ana Jeremías López,Joseph Lipman
Studies in Duality on Noetherian Formal Schemes and Non Noetherian Ordinary Schemes Book PDF

Author : Leovigildo Alonso Tarrío,Leovigildo Alonso,Ana Jeremías López,Joseph Lipman
Publisher : American Mathematical Soc.
Page : 138 pages
File Size : 51,6 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.

Variance and Duality for Cousin Complexes on Formal Schemes

Joseph Lipman,Suresh Nayak,Pramathanath Sastry
Variance and Duality for Cousin Complexes on Formal Schemes Book PDF

Author : Joseph Lipman,Suresh Nayak,Pramathanath Sastry
Publisher : American Mathematical Soc.
Page : 276 pages
File Size : 49,9 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821837054

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Variance and Duality for Cousin Complexes on Formal Schemes by Joseph Lipman,Suresh Nayak,Pramathanath Sastry Pdf

Robert Hartshorne's 1966 book, Residues and Duality, introduced the notion of residual complexes and developed a duality theory (Grothendieck duality) on the category of maps of noetherian schemes. The three articles in this volume constitute a reworking of the main parts of the corresponding chapters in Hartshorne's 1966 book in greater generality using a somewhat different approach. Additionally, the authors' motivation is to help readers gain a better understanding of the relation between local properties of residues and global properties of the dualizing pseudofunctor. The book is suitable for graduate students and researchers working in algebraic geometry.

Integral Domains Inside Noetherian Power Series Rings: Constructions and Examples

William Heinzer,Christel Rotthaus,Sylvia Wiegand
Integral Domains Inside Noetherian Power Series Rings Constructions and Examples Book PDF

Author : William Heinzer,Christel Rotthaus,Sylvia Wiegand
Publisher : American Mathematical Soc.
Page : 426 pages
File Size : 54,7 Mb
Release : 2021-10-08
Category : Education
ISBN : 9781470466428

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Integral Domains Inside Noetherian Power Series Rings: Constructions and Examples by William Heinzer,Christel Rotthaus,Sylvia Wiegand Pdf

Power series provide a technique for constructing examples of commutative rings. In this book, the authors describe this technique and use it to analyse properties of commutative rings and their spectra. This book presents results obtained using this approach. The authors put these results in perspective; often the proofs of properties of classical examples are simplified. The book will serve as a helpful resource for researchers working in commutative algebra.

Triangulated Categories

Thorsten Holm,Peter Jørgensen,Raphaël Rouquier
Triangulated Categories Book PDF

Author : Thorsten Holm,Peter Jørgensen,Raphaël Rouquier
Publisher : Cambridge University Press
Page : 473 pages
File Size : 50,8 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.

Grothendieck Duality and Base Change

Brian Conrad
Grothendieck Duality and Base Change Book PDF

Author : Brian Conrad
Publisher : Springer
Page : 300 pages
File Size : 42,5 Mb
Release : 2003-07-01
Category : Mathematics
ISBN : 9783540400158

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Grothendieck Duality and Base Change by Brian Conrad Pdf

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.

Residues and Duality for Projective Algebraic Varieties

Ernst Kunz
Residues and Duality for Projective Algebraic Varieties Book PDF

Author : Ernst Kunz
Publisher : American Mathematical Soc.
Page : 177 pages
File Size : 54,5 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.

K-theory in Algebra, Analysis and Topology

Guillermo Cortiñas,Charles A. Weibel
K theory in Algebra Analysis and Topology Book PDF

Author : Guillermo Cortiñas,Charles A. Weibel
Publisher : American Mathematical Soc.
Page : 388 pages
File Size : 51,9 Mb
Release : 2024-06-15
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.

Real and Complex Singularities

Laurentiu Paunescu
Real and Complex Singularities Book PDF

Author : Laurentiu Paunescu
Publisher : World Scientific
Page : 475 pages
File Size : 50,9 Mb
Release : 2007
Category : Science
ISBN : 9789812705518

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Real and Complex Singularities by Laurentiu Paunescu Pdf

The modern theory of singularities provides a unifying theme that runs through fields of mathematics as diverse as homological algebra and Hamiltonian systems. It is also an important point of reference in the development of a large part of contemporary algebra, geometry and analysis. Presented by internationally recognized experts, the collection of articles in this volume yields a significant cross-section of these developments. The wide range of surveys includes an authoritative treatment of the deformation theory of isolated complex singularities by prize-winning researcher K Miyajima. Graduate students and even ambitious undergraduates in mathematics will find many research ideas in this volume and non-experts in mathematics can have an overview of some classic and fundamental results in singularity theory. The explanations are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to go further into the subject and explore the research literature.

Building Bridges Between Algebra and Topology

Wojciech Chachólski,Tobias Dyckerhoff,John Greenlees,Greg Stevenson
Building Bridges Between Algebra and Topology Book PDF

Author : Wojciech Chachólski,Tobias Dyckerhoff,John Greenlees,Greg Stevenson
Publisher : Birkhäuser
Page : 225 pages
File Size : 41,8 Mb
Release : 2018-03-31
Category : Mathematics
ISBN : 9783319701578

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Building Bridges Between Algebra and Topology by Wojciech Chachólski,Tobias Dyckerhoff,John Greenlees,Greg Stevenson Pdf

This volume presents an elaborated version of lecture notes for two advanced courses: (Re)Emerging methods in Commutative Algebra and Representation Theory and Building Bridges Between Algebra and Topology, held at the CRM in the spring of 2015. Homological algebra is a rich and ubiquitous area; it is both an active field of research and a widespread toolbox for many mathematicians. Together, these notes introduce recent applications and interactions of homological methods in commutative algebra, representation theory and topology, narrowing the gap between specialists from different areas wishing to acquaint themselves with a rapidly growing field. The covered topics range from a fresh introduction to the growing area of support theory for triangulated categories to the striking consequences of the formulation in the homotopy theory of classical concepts in commutative algebra. Moreover, they also include a higher categories view of Hall algebras and an introduction to the use of idempotent functors in algebra and topology.

Interactions between Homotopy Theory and Algebra

Summer School on Interactions between Homotopy Theory and Algebra
Interactions between Homotopy Theory and Algebra Book PDF

Author : Summer School on Interactions between Homotopy Theory and Algebra
Publisher : American Mathematical Soc.
Page : 352 pages
File Size : 41,8 Mb
Release : 2007
Category : Commutative algebra
ISBN : 9780821838143

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Interactions between Homotopy Theory and Algebra by Summer School on Interactions between Homotopy Theory and Algebra Pdf

This book is based on talks presented at the Summer School on Interactions between Homotopy theory and Algebra held at the University of Chicago in the summer of 2004. The goal of this book is to create a resource for background and for current directions of research related to deep connections between homotopy theory and algebra, including algebraic geometry, commutative algebra, and representation theory. The articles in this book are aimed at the audience of beginning researchers with varied mathematical backgrounds and have been written with both the quality of exposition and the accessibility to novices in mind.

Applications of Curves Over Finite Fields

Joint Summ Ams-Ims-Siam,Michael D. Fried,AMS-IMS-SIAM Joint Summer Research Conference on Applications of Curves over Finite Fields,Ams-Ims-Siam Joint Summer Research Conference on Applications of curve
Applications of Curves Over Finite Fields Book PDF

Author : Joint Summ Ams-Ims-Siam,Michael D. Fried,AMS-IMS-SIAM Joint Summer Research Conference on Applications of Curves over Finite Fields,Ams-Ims-Siam Joint Summer Research Conference on Applications of curve
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 42,9 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821809259

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Applications of Curves Over Finite Fields by Joint Summ Ams-Ims-Siam,Michael D. Fried,AMS-IMS-SIAM Joint Summer Research Conference on Applications of Curves over Finite Fields,Ams-Ims-Siam Joint Summer Research Conference on Applications of curve Pdf

This volume presents the results of the AMS-IMS-SIAM Joint Summer Research Conference held at the University of Washington (Seattle). The talks were devoted to various aspects of the theory of algebraic curves over finite fields and its numerous applications. The three basic themes are the following: Curves with many rational points. Several articles describe main approaches to the construction of such curves: the Drinfeld modules and fiber product methods, the moduli space approach, and the constructions using classical curves; Monodromy groups of characteristic $p$ covers. A number of authors presented the results and conjectures related to the study of the monodromy groups of curves over finite fields. In particular, they study the monodromy groups from genus $0$ covers, reductions of covers, and explicit computation of monodromy groups over finite fields; and, Zeta functions and trace formulas.To a large extent, papers devoted to this topic reflect the contributions of Professor Bernard Dwork and his students. This conference was the last attended by Professor Dwork before his death, and several papers inspired by his presence include commentaries about the applications of trace formulas and $L$-function. The volume also contains a detailed introduction paper by Professor Michael Fried, which helps the reader to navigate in the material presented in the book.

Structured Matrices in Mathematics, Computer Science, and Engineering II

Vadim Olshevsky
Structured Matrices in Mathematics Computer Science and Engineering II Book PDF

Author : Vadim Olshevsky
Publisher : American Mathematical Soc.
Page : 362 pages
File Size : 49,8 Mb
Release : 2001
Category : Matrices
ISBN : 9780821820926

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Structured Matrices in Mathematics, Computer Science, and Engineering II by Vadim Olshevsky Pdf

"The collection of the contributions to these volumes offers a flavor of the plethora of different approaches to attack structured matrix problems. The reader will find that the theory of structured matrices is positioned to bridge diverse applications in the sciences and engineering, deep mathematical theories, as well as computational and numberical issues. The presentation fully illustrates the fact that the technicques of engineers, mathematicisn, and numerical analysts nicely complement each other, and they all contribute to one unified theory of structured matrices"--Back cover.

Radon Transforms and Tomography

Eric Todd Quinto
Radon Transforms and Tomography Book PDF

Author : Eric Todd Quinto
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 41,7 Mb
Release : 2001
Category : Radon transforms
ISBN : 9780821821350

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Radon Transforms and Tomography by Eric Todd Quinto Pdf

One of the most exciting features of the fields of Radon transforms and tomography is the strong relationship between high-level pure mathematics and applications to areas such as medical imaging and industrial nondestructive evaluation. The proceedings featured in this volume bring together fundamental research articles in the major areas of Radon transforms and tomography. This volume includes expository papers that are of special interest to beginners as well as advanced researchers. Topics include local tomography and wavelets, Lambda tomography and related methods, tomographic methods in RADAR, ultrasound, Radon transforms and differential equations, and the Pompeiu problem. The major themes in Radon transforms and tomography are represented among the research articles. Pure mathematical themes include vector tomography, microlocal analysis, twistor theory, Lie theory, wavelets, harmonic analysis, and distribution theory. The applied articles employ high-quality pure mathematics to solve important practical problems. Effective scanning geometries are developed and tested for a NASA wind tunnel. Algorithms for limited electromagnetic tomographic data and for impedance imaging are developed and tested. Range theorems are proposed to diagnose problems with tomography scanners. Principles are given for the design of X-ray tomography reconstruction algorithms, and numerical examples are provided. This volume offers readers a comprehensive source of fundamental research useful to both beginners and advanced researchers in the fields.

Homotopy Methods in Algebraic Topology

Nicholas Kuhn
Homotopy Methods in Algebraic Topology Book PDF

Author : Nicholas Kuhn
Publisher : American Mathematical Soc.
Page : 370 pages
File Size : 47,6 Mb
Release : 2001-04-25
Category : Algebraic topology
ISBN : 9780821826218

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Homotopy Methods in Algebraic Topology by Nicholas Kuhn Pdf

This volume presents the proceedings from the AMS-IMS-SIAM Summer Research Conference on Homotopy Methods in Algebraic Topology held at the University of Colorado (Boulder). The conference coincided with the sixtieth birthday of J. Peter May. An article is included reflecting his wide-ranging and influential contributions to the subject area. Other articles in the book discuss the ordinary, elliptic and real-oriented Adams spectral sequences, mapping class groups, configuration spaces, extended powers, operads, the telescope conjecture, $p$-compact groups, algebraic K theory, stable and unstable splittings, the calculus of functors, the $E_{\infty}$ tensor product, and equivariant cohomology theories. The book offers a compendious source on modern aspects of homotopy theoretic methods in many algebraic settings.

Nonlinear PDE's, Dynamics and Continuum Physics

J. L. Bona,Katarzyna Saxton,Ralph Saxton
Nonlinear PDE s Dynamics and Continuum Physics Book PDF

Author : J. L. Bona,Katarzyna Saxton,Ralph Saxton
Publisher : American Mathematical Soc.
Page : 270 pages
File Size : 51,8 Mb
Release : 2000
Category : Continuum mechanics
ISBN : 9780821810521

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Nonlinear PDE's, Dynamics and Continuum Physics by J. L. Bona,Katarzyna Saxton,Ralph Saxton Pdf

This volume contains the refereed proceedings of the conference on Nonlinear Partial Differential Equations, Dynamics and Continuum Physics which was held at Mount Holyoke College in Massachusetts, from July 19th to July 23rd, 1998. Models examined derive from a wide range of applications, including elasticity, thermoviscoelasticity, granular media, fluid dynamics, gas dynamics and conservation laws. Mathematical topics include existence theory and stability/instability of traveling waves, asymptotic behavior of solutions to nonlinear wave equations, effects of dissipation, mechanisms of blow-up, well-posedness and regularity, and fractal solutions. The text will be of interest to graduate students and researchers working in nonlinear partial differential equations and applied mathematics.