LEADER 04654nam 2200601 450 001 9910480637303321 005 20170822123752.0 010 $a1-4704-0309-9 035 $a(CKB)3360000000464900 035 $a(EBL)3114407 035 $a(SSID)ssj0000976564 035 $a(PQKBManifestationID)11528130 035 $a(PQKBTitleCode)TC0000976564 035 $a(PQKBWorkID)11019711 035 $a(PQKB)11125111 035 $a(MiAaPQ)EBC3114407 035 $a(PPN)195416023 035 $a(EXLCZ)993360000000464900 100 $a20010109d2001 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aStable homotopy over the Steenrod algebra /$fJohn H. Palmieri 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2001. 215 $a1 online resource (193 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 716 300 $a"Volume 151, number 716 (second of 5 numbers)." 311 $a0-8218-2668-9 320 $aIncludes bibliographical references and index. 327 $a""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(I??)""; ""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"" 327 $a""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"" 327 $a""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"" 327 $a""4.6.1. Computation of (Q[sub(n)])[sub(**)](Q[sub(n)])""""4.6.2. Eisen's calculation""; ""4.6.3. The I??[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"" 327 $a""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"" 327 $a""6.8. Further discussion: slope supports"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 716. 606 $aHomotopy theory 606 $aSteenrod algebra 608 $aElectronic books. 615 0$aHomotopy theory. 615 0$aSteenrod algebra. 676 $a510 s 676 $a514/.24 700 $aPalmieri$b John H$g(John Harold),$f1964-$0917929 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480637303321 996 $aStable homotopy over the Steenrod algebra$92058231 997 $aUNINA