Phantom Homology

Phantom Homology

Author: Melvin Hochster

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 105

ISBN-13: 0821825569

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This book uses a powerful new technique, tight closure, to provide insight into many different problems that were previously not recognized as related. The authors develop the notion of weakly Cohen-Macaulay rings or modules and prove some very general acyclicity theorems. These theorems are applied to the new theory of phantom homology, which uses tight closure techniques to show that certain elements in the homology of complexes must vanish when mapped to well-behaved rings. These ideas are used to strengthen various local homological conjectures. Initially, the authors develop the theory in positive characteristic, but it can be extended to characteristic 0 by the method of reduction to characteristic $p$. The book would be suitable for use in an advanced graduate course in commutative algebra.


Stable and Unstable Homotopy

Stable and Unstable Homotopy

Author: William G. Dwyer

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 326

ISBN-13: 0821808249

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This volume presents the proceedings of workshops on stable homotopy theory and on unstable homotopy theory held at The Field Institute as part of the homotopy program for the year 1996. The papers in the volume describe current research in the subject, and all included works were refereed. Rather than being a summary of work to be published elsewhere, each paper is the unique source for the new material it contains. The book contains current research from international experts in the subject area, and presents open problems with directions for future research.


Tight Closure and Its Applications

Tight Closure and Its Applications

Author: Craig Huneke

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 152

ISBN-13: 082180412X

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This monograph deals with the theory of tight closure and its applications. The contents are based on ten talks given at a CBMS conference held at North Dakota State University in June 1995.


Commutative Algebra

Commutative Algebra

Author: Melvin Hochster

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 516

ISBN-13: 1461236606

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During late June and early July of 1987 a three week program (dubbed "microprogram") in Commutative Algebra was held at the Mathematical Sciences Research Institute at Berkeley. The intent of the microprogram was to survey recent major results and current trends in the theory of commutative rings, especially commutative Noetherian rings. There was enthusiastic international participation. The papers in this volume, some of which are expository, some strictly research, and some a combination, reflect the intent of the program. They give a cross-section of what is happening now in this area. Nearly all of the manuscripts were solicited from the speakers at the conference, and in most instances the manuscript is based on the conference lecture. The editors hope that they will be of interest and of use both to experts and neophytes in the field. The editors would like to express their appreciation to the director of MSRI, Professor Irving Kaplansky, who first suggested the possibility of such a conference and made the task of organization painless. We would also like to thank the IVISRI staff who were unfailingly efficient, pleasant, and helpful during the meeting, and the manager of MSRI, Arlene Baxter, for her help with this volume. Finally we would like to express our appreciation to David Mostardi who did much of the typing and put the electronic pieces together.


Women in Commutative Algebra

Women in Commutative Algebra

Author: Claudia Miller

Publisher: Springer Nature

Published: 2022-03-18

Total Pages: 439

ISBN-13: 3030919862

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This volume features contributions from the Women in Commutative Algebra (WICA) workshop held at the Banff International Research Station (BIRS) from October 20-25, 2019, run by the Pacific Institute of Mathematical Sciences (PIMS). The purpose of this meeting was for groups of mathematicians to work on joint research projects in the mathematical field of Commutative Algebra and continue these projects together long-distance after its close. The chapters include both direct results and surveys, with contributions from research groups and individual authors. The WICA conference was the first of its kind in the large and vibrant area of Commutative Algebra, and this volume is intended to showcase its important results and to encourage further collaboration among marginalized practitioners in the field. It will be of interest to a wide range of researchers, from PhD students to senior experts.


Representations of Algebras and Related Topics

Representations of Algebras and Related Topics

Author: Ragnar-Olaf Buchweitz

Publisher: American Mathematical Soc.

Published: 2005

Total Pages: 418

ISBN-13: 0821834150

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Twelve-year-old Molly and her ten-year-old brother, Michael, have never liked their younger stepsister, Heather. Ever since their parents got married, she's made Molly and Michael's life miserable. Now their parents have moved them all to the country to live in a house that used to be a church, with a cemetery in the backyard. If that's not bad enough, Heather starts talking to a ghost named Helen and warning Molly and Michael that Helen is coming for them. Molly feels certain Heather is in some kind of danger, but every time she tries to help, Heather twists things around to get her into trouble. It seems as if things can't get any worse. But they do -- when Helen comes. "Genuinely scary, complete with dark secrets from the past, unsettled graves, and a very real ghost." -- The Bulletin of the Center for Children's Books "An unusually scary, well-crafted ghost fantasy." -- Kirkus Reviews


Continuous Images of Arcs and Inverse Limit Methods

Continuous Images of Arcs and Inverse Limit Methods

Author: Jacek Nikiel

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 95

ISBN-13: 0821825615

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Continuous images of ordered continua are investigated. The paper gives various properties of their monotone images and inverse limits of their inverse systems (or sequences) with monotone bonding surjections. Some factorization theorems are provided. Special attention is given to one-dimensional spaces which are continuous images of arcs and, among them, various classes of rim-finite continua. The methods of proofs include cyclic element theory, T-set approximations and null-family decompositions. The paper brings also new properties of cyclic elements and T-sets in locally connected continua, in general.


Symplectic Cobordism and the Computation of Stable Stems

Symplectic Cobordism and the Computation of Stable Stems

Author: Stanley O. Kochman

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 105

ISBN-13: 0821825585

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This memoir consists of two independent papers. In the first, "The symplectic cobordism ring III" the classical Adams spectral sequence is used to study the symplectic cobordism ring [capital Greek]Omega[superscript]* [over] [subscript italic capital]S[subscript italic]p. In the second, "The symplectic Adams Novikov spectral sequence for spheres" we analyze the symplectic Adams-Novikov spectral sequence converging to the stable homotopy groups of spheres.


The Kinematic Formula in Riemannian Homogeneous Spaces

The Kinematic Formula in Riemannian Homogeneous Spaces

Author: Ralph Howard

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 82

ISBN-13: 0821825690

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This memoir investigates a method that generalizes the Chern-Federer kinematic formula to arbitrary homogeneous spaces with an invariant Riemannian metric, and leads to new formulas even in the case of submanifolds of Euclidean space.