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Stable homotopy over the Steenrod algebra / / John H. Palmieri
| Stable homotopy over the Steenrod algebra / / John H. Palmieri |
| Autore | Palmieri John H (John Harold), <1964-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2001 |
| Descrizione fisica | 1 online resource (193 p.) |
| Disciplina |
510 s
514/.24 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Homotopy theory
Steenrod algebra |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0309-9 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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(Î?)""; ""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 Ï?[sub(1)]-inverted Ext of the mod 2 Moore spectrum""; ""Chapter 5. Quillen stratification and nilpotence""; ""5.1. Statements of theorems""; ""5.1.1. 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"" |
| Record Nr. | UNINA-9910480637303321 |
Palmieri John H (John Harold), <1964->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Stable homotopy over the Steenrod algebra / / John H. Palmieri
| Stable homotopy over the Steenrod algebra / / John H. Palmieri |
| Autore | Palmieri John H (John Harold), <1964-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2001 |
| Descrizione fisica | 1 online resource (193 p.) |
| Disciplina |
510 s
514/.24 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Homotopy theory
Steenrod algebra |
| ISBN | 1-4704-0309-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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(Î?)""; ""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 Ï?[sub(1)]-inverted Ext of the mod 2 Moore spectrum""; ""Chapter 5. Quillen stratification and nilpotence""; ""5.1. Statements of theorems""; ""5.1.1. 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"" |
| Record Nr. | UNINA-9910788843503321 |
|
Palmieri John H (John Harold), <1964->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Stable homotopy over the Steenrod algebra / / John H. Palmieri
| Stable homotopy over the Steenrod algebra / / John H. Palmieri |
| Autore | Palmieri John H (John Harold), <1964-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2001 |
| Descrizione fisica | 1 online resource (193 p.) |
| Disciplina |
510 s
514/.24 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Homotopy theory
Steenrod algebra |
| ISBN | 1-4704-0309-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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(Î?)""; ""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 Ï?[sub(1)]-inverted Ext of the mod 2 Moore spectrum""; ""Chapter 5. Quillen stratification and nilpotence""; ""5.1. Statements of theorems""; ""5.1.1. 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"" |
| Record Nr. | UNINA-9910813654803321 |
|
Palmieri John H (John Harold), <1964->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||