# Phantom homology

by Melvin Hochster

Publisher: American Mathematical Society in Providence, R.I

Written in English

## Subjects:

• Noetherian rings.,
• Complexes.,
• Modules (Algebra)

## Edition Notes

Classifications The Physical Object Statement Melvin Hochster, Craig Huneke. Series Memoirs of the American Mathematical Society,, no. 490 Contributions Huneke, C. LC Classifications QA3 .A57 no. 490, QA251.3 .A57 no. 490 Pagination vi, 91 p. ; Number of Pages 91 Open Library OL1393317M ISBN 10 0821825569 LC Control Number 93000463

Let X and Y be connected nilpotent CW–complexes of finite type. In this paper we deal with another complete analysis of a set of phantom maps in terms of strong homology by using the derived. E-book $to$ About E-books ISBN: Published December With firm foundations dating only from the s, algebraic topology is a relatively young area of mathematics. There are very few textbooks that treat fundamental topics beyond a first course, and many topics now essential to the field are not treated in any. A is the universal example of a homology theory with values in an AB 5 category and compare this with some results of Freyd. Contents 1. Introduction 1 2. Axiomatic stable homotopy theory 4 3. Homology theories 6 4. Phantom maps 9 5. Margolis's axiomatisation conjecture 15 6. Phantom cohomology 16 7. Universal homology theories @MISC{Daniel98phantommaps, author = {J. Daniel and Christensen and Neil P. Strickland}, title = {PHANTOM MAPS AND HOMOLOGY THEORIES}, year = {}} Share. OpenURL. Abstract. Abstract. We study phantom maps and homology theories in a stable homotopy. Keyphrases.

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C. McGibbon, Phantom maps,in Handbook of Algebraic Topology, North-Holland, Amsterdam, , pp. – [34] A. Mekler and S. Shelah, Every coseparable group may be free, Israel Journal of Mathematics 81 (), – [35] J. Milnor, On axiomatic homology theory, Paciﬁc Journal of Mathematics 12 (), – [36] M. jojos bizarre adventure part 1 phantom blood vol 2 Posted By Nora Roberts Publishing TEXT ID Online PDF Ebook Epub Library notified when this product is available notify me quantity add to cart free us shipping get more with premium up to 25 off you purchase and access to unlimited ad free. Melvin Hochster (born August 2, ) is an American mathematician working in commutative is currently the Jack E. McLaughlin Distinguished University Professor of Mathematics at . The Phantom is a Australian-American superhero film directed by Simon on Lee Falk's comic strip The Phantom by King Features, the film stars Billy Zane as a seemingly immortal crimefighter and his battle against all forms of evil. The Phantom also stars Treat Williams, Kristy Swanson, Catherine Zeta-Jones, James Remar and Patrick McGoohan.

## Recent

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.

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. Introduction --Minheight and the weak Cohen-Macaulay property --Acyclicity criteria with denominators for complexes of modules --Vanishing theorems for maps of homology via phantom acyclicity --Regular closure --Intersection theorems via phantom acyclicity.

Series Title: Memoirs of the American Mathematical Society, no. Responsibility. Introduction 2. Minheight and the weak Cohen-Macaulay property 3. Acyclicity criteria with denominators for complexes of modules 4. Vanishing theorems for maps of homology via phantom acyclicity 5.

Regular closure 6. Intersection theorems via phantom acyclicity. Series Title: Memoirs of the American Mathematical Society, no. Responsibility. Basic information concerning the Hilbert-Kunz function, phantom homology, and regular base change for tight closure.

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The writing is extremely undeveloped. It truly does seem as if it was written by someone about the age of I'm sorry but I can't recommend s: 5. The Phantom is a comic strip created by Lee Falk (also creator of Mandrake the Magician), recounting the adventures of a costumed crime-fighter called the series began with a daily newspaper strip on Februwhich was joined by a color Sunday strip in May of ; both are still running as of and are read by millions of people every day.

Basic information concerning the Hilbert-Kunz function, phantom homology, and regular base change for tight closure. Numerous exercises with solutions. Inspire a love of reading with Prime Book Box for Kids Discover delightful children's books with Prime Book Box, a subscription that delivers new books every 1, 2, or 3 months — new customers Author: Craig Huneke.

We study phantom maps and homology theories in a stable homotopy category S via a certain Abelian category express the group P (X, Y) of phantom maps X → Y as an Ext group in A, and give conditions on X or Y which guarantee that it vanishes.

We also determine P (X, HB).We show that any composite of two phantom maps is zero, and use this to reduce Margolis's axiomatisation. The Phantom is an American adventure comic strip, first published by Lee Falk in February The main character, the Phantom, is a fictional costumed crime-fighter who operates from the fictional African country of character has been adapted for television, film and video games.

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contractible) space is canonically isomorphic to singular cohomology of a CW-complex (the nerve of the poset of suitable open subspaces), hence coincides. Journals & Books; Help Three partial sequences with high homology to Bombyx phm, (nvd), spook, phantom, and disembodied but not non-molting glossy and shadow.

Furthermore, JHA application reduced the amount of 7-dehydrocholesterol, a metabolite produced by Nvd, in both the prothoracic glands and hemolymph, indicating JHA can disrupt.

A is the universal example of a homology theory with values in an AB 5 category and compare this with some results of Freyd. Contents 1. Introduction 1 2. Axiomatic stable homotopy theory 4 3. Homology theories 6 4. Phantom maps 9 5.

Margolis's axiomatisation conjecture 15 6. Phantom cohomology 16 7. Universal homology theories 21 References 25 1.Twenty-sixth in a series of clips from the film version of The Phantom of the Opera. As told by Miranda Richardson a.Indeed, they induce the trivial homomorphism on homotopy groups, in homology, and in cohomology.

The chapter also highlights the spaces in which all phantom maps are trivial.