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001			EBC3114407
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005			20240729124607.0
006			m o d |
007			cr cnu||||||||
008			240724s2001 xx o ||||0 eng d
020			_a9781470403096 _q(electronic bk.)
020			_z9780821826683
035			_a(MiAaPQ)EBC3114407
035			_a(Au-PeEL)EBL3114407
035			_a(CaPaEBR)ebr11041185
035			_a(OCoLC)922964890
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA612.7 -- .P35 2001eb
082	0		_a510 s;514/.24
100	1		_aPalmieri, John H.
245	1	0	_aStable Homotopy over the Steenrod Algebra.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2001.
264		4	_c©2001.
300			_a1 online resource (193 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.151
505	0		_aIntro -- Contents -- List of Figures -- Preface -- Chapter 0. Preliminaries -- 0.1. Grading and other conventions -- 0.2. Hopf algebras -- 0.3. Modules and comodules -- 0.4. Homological algebra -- 0.5. Two small examples -- Chapter 1. Stable homotopy over a Hopf algebra -- 1.1. The category Stable(Γ) -- 1.2. The functor H -- 1.2.1. Remarks on Hopf algebra extensions -- 1.3. Some classical homotopy theory -- 1.4. The Adams spectral sequence -- 1.5. Bousfield classes and Brown-Comenetz duality -- 1.6. Further discussion -- Chapter 2. Basic properties of the Steenrod algebra -- 2.1. Quotient Hopf algebras of A -- 2.1.1. Quasi-elementary quotients of A -- 2.2. P[sup(s)][sub(t)]-homology -- 2.2.1. Miscellaneous results about P[sup(s)][sub(t)]-homology -- 2.3. Vanishing lines for homotopy groups -- 2.3.1. Proof of Theorems 2.3.1 and 2.3.2 when p = 2 -- 2.3.2. Changes necessary when p is odd -- 2.4. Self-maps via vanishing lines -- 2.5. Construction of spectra of specified type -- 2.6. Further discussion -- Chapter 3. Chromatic structure -- 3.1. Margolis' killing construction -- 3.2. A Tate version of the functor H -- 3.3. Chromatic convergence -- 3.4. Further discussion: work of Mahowald and Shick -- 3.5. Further discussion -- Chapter 4. Computing Ext with elements inverted -- 4.1. The q[sub(n)]-based Adams spectral sequence -- 4.2. The Q[sub(n)]-based Adams spectral sequence -- 4.3. A(n) as an A-comodule -- 4.4. 1/2A(n) satisfies the vanishing plane condition -- 4.5. 1/2A(n) generates the expected thick subcategory -- 4.5.1. The proof of Proposition 4.5.7 -- 4.6. Some computations and applications -- 4.6.1. Computation of (Q[sub(n)])[sub(**)](Q[sub(n)]) -- 4.6.2. Eisen's calculation -- 4.6.3. The υ[sub(1)]-inverted Ext of the mod 2 Moore spectrum -- Chapter 5. Quillen stratification and nilpotence -- 5.1. Statements of theorems.
505	8		_a5.1.1. Quillen stratification -- 5.1.2. Nilpotence -- 5.2. Nilpotence and F-isomorphism via the Hopf algebra D -- 5.2.1. Nilpotence: Proof of Theorem 5.1.5 -- 5.2.2. F-isomorphism: Proof of Theorem 5.1.2 -- 5.3. Nilpotence and F-isomorphism via quasi-elementary quotients -- 5.3.1. Nilpotence: Proof of Theorem 5.1.6 -- 5.3.2. F-isomorphism: Proof of Theorem 5.1.3 -- 5.4. Further discussion: nilpotence at odd primes -- 5.5. Further discussion: miscellany -- Chapter 6. Periodicity and other applications of the nilpotence theorems -- 6.1. The periodicity theorem -- 6.2. y-maps and their properties -- 6.3. Properties of ideals -- 6.4. The proof of the periodicity theorem -- 6.5. Computation of some invariants in HD[sub(**)] -- 6.6. Computation of a few Bousfield classes -- 6.7. Ideals and thick subcategories -- 6.7.1. The thick subcategory conjecture -- 6.7.2. Rank varieties -- 6.8. Further discussion: slope supports -- 6.9. Further discussion: miscellany -- Appendix A. An underlying model category -- Appendix B. Steenrod operations and nilpotence in Ext**[sub(Γ)] (k,k) -- B.1. Steenrod operations in Hopf algebra cohomology -- B.2. Nilpotence in Ext over quotients of A: p = 2 -- B.3. Nilpotence in Ext over quotients of A: p odd -- B.3.1. Sketch of proof of Conjecture B.3.4, and other results -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- P -- Q -- R -- S -- T -- U -- V -- W -- X -- Y -- Z.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aHomotopy theory.
650		0	_aSteenrod algebra.
655		4	_aElectronic books.
776	0	8	_iPrint version: _aPalmieri, John H. _tStable Homotopy over the Steenrod Algebra _dProvidence : American Mathematical Society,c2001 _z9780821826683
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114407 _zClick to View
999			_c69902 _d69902