Phantom homology

by Melvin Hochster

Publisher: American Mathematical Society in Providence, R.I

Written in English
Cover of: Phantom homology | Melvin Hochster
Published: Pages: 91 Downloads: 908
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Subjects:

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

Edition Notes

StatementMelvin Hochster, Craig Huneke.
SeriesMemoirs of the American Mathematical Society,, no. 490
ContributionsHuneke, C.
Classifications
LC ClassificationsQA3 .A57 no. 490, QA251.3 .A57 no. 490
The Physical Object
Paginationvi, 91 p. ;
Number of Pages91
ID Numbers
Open LibraryOL1393317M
ISBN 100821825569
LC Control Number93000463

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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Phantom homology by Melvin Hochster Download PDF EPUB FB2

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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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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In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups associated to a topological space, often defined from a cochain logy can be viewed as a method of assigning richer algebraic invariants to a space than homology.

Some versions of cohomology arise by dualizing the construction of homology. homology. spectral sequence. This page collects material and links related to. Ioan Mackenzie James, The Handbook of Algebraic Topology.

Oxford Phantom maps (C.A. McGibbon). Wall’s finiteness obstruction (G. Mislin). Lusternik-Schnirelmann category (I.M. James). Related entries. phantom M-regular sequences in all cases of interest (see Proposition ) but are often easier to use than the latter.

With these tools, I obtain characterizations of phantom depth (Theorem ) and phantom M-regular sequences (Theorem ) in terms of stable phantomness, rather than vanishing, of Koszul homology. These include the existence of big Cohen-Macaulay algebras and various uniform Artin-Rees features: the existence of test elements; a study of F-rational rings and rational singularities; basic information concerning the Hilbert-Kunz function, phantom homology, and regular base change for tight closure; and, numerous exercises with.

$\begingroup$ I have tried to give (a little) more references about the existence of pro-adjoints above. The idea is that, using the functor {infinity-topoi}->Pro(S), one sees that sheaf-theoretic singular (co)homology of a locally nice (e.g.

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.