Axiomatic, enriched and motivic homotopy theory

Contents......Page page000004.djvu
Contributing Authors......Page page000008.djvu
Preface......Page page000010.djvu
1. Introduction......Page page000014.djvu
2. Algebra......Page page000018.djvu
3. Homological localization in topology......Page page000021.djvu
4. Localization with respect to a map......Page page000024.djvu
5. Colocalization with respect to an object......Page page000031.djvu
6. Higher invariants of localization......Page page000033.djvu
7. Constructing localizations and colocalizations......Page page000035.djvu
References......Page page000037.djvu
Generalised sheaf cohomology theories (J. F. Jardine)......Page page000040.djvu
1. Simplicial presheaves......Page page000041.djvu
2. Presheaves of spectra......Page page000054.djvu
3. Profini te groups......Page page000062.djvu
4. Generalised Galois cohomology theory......Page page000066.djvu
5. Thomason\'s descent theorem......Page page000073.djvu
References......Page page000077.djvu
1. Introduction......Page page000080.djvu
2. Axioms......Page page000083.djvu
4. Types of subcategories......Page page000091.djvu
5. Quotient categories and Bousfield localisation......Page page000095.djvu
6. Versions of the Bousfield lattice......Page page000096.djvu
7. Special types of localisation......Page page000098.djvu
8. Nilpotence......Page page000100.djvu
9. Brown represent ability......Page page000102.djvu
References......Page page000105.djvu
Pre-)Sheaves of Ring Spectra over the Moduli Stack of Formal Group Laws (Paul G. Goerss)......Page page000112.djvu
1. The Realization Problem......Page page000113.djvu
2. Moduli Spaces and Obstruction Theory......Page page000127.djvu
References......Page page000140.djvu
1. Introduction......Page page000144.djvu
2. Loop spaces and the little intervals operad......Page page000146.djvu
3. Cosimplicial objects and totalization......Page page000151.djvu
4. A sufficient condition for Tot(X) to be an A_∞ space......Page page000154.djvu
5. A reformulation......Page page000157.djvu
6. Operads......Page page000158.djvu
7. A family of cochain operations......Page page000160.djvu
8. A sufficient condition for Tot(X) to be an E_∞ space......Page page000162.djvu
9. The little n-cubes operad......Page page000165.djvu
10. A sufficient condition for Tot(X) to be an E_n space......Page page000168.djvu
11. An extension of Remark 6.3(b)......Page page000170.djvu
12. Proof of Theorem 10.6......Page page000172.djvu
13. Applications......Page page000173.djvu
14. The framed little disks operad......Page page000174.djvu
15. Cosimplicial chain complexes......Page page000176.djvu
16. Applications......Page page000179.djvu
References......Page page000180.djvu
From HAG to DAG: derived moduli stacks (Bertrand Toen, Gabriele Vezzosi)......Page page000184.djvu
1. Introduction......Page page000185.djvu
2. The model category of D-stacks......Page page000193.djvu
3. First examples of D-stacks......Page page000200.djvu
4. The geometry of D-stacks......Page page000207.djvu
5. Further examples......Page page000217.djvu
References......Page page000225.djvu
1. Introduction: homotopy theory and differential topology......Page page000230.djvu
2. From smooth varieties to spaces......Page page000236.djvu
3. Stable homotopy categories of S¹-spectra......Page page000242.djvu
4. The A¹-homotopy t-structure and the stable Hurewicz theorem......Page page000247.djvu
5. Inverting ℙ¹......Page page000254.djvu
6. π₀(S⁰) and Milnor-Witt K theory of fields......Page page000262.djvu
References......Page page000270.djvu
0. Introduction......Page page000272.djvu
1. Oriented cohomology pretheories......Page page000277.djvu
2. Riemann- Roch type theorems......Page page000305.djvu
References......Page page000341.djvu
1. Introduction......Page page000346.djvu
2. Classical Motives......Page page000347.djvu
3. Equivariant Motives......Page page000352.djvu
4. The Gross-Stark Conjecture......Page page000363.djvu
5. The fractional ideal I^r_F......Page page000365.djvu
6. New Conjectures......Page page000370.djvu
7. Supporting evidence......Page page000372.djvu
8. Annihilators and K₀(ℤ[G], ℚ_l)......Page page000375.djvu
9. The Lichtenbaum conjecture......Page page000382.djvu
10. Relation to Vandiver\'s Conjecture......Page page000387.djvu
References......Page page000390.djvu
2. Motivic Homotopy Theory......Page page000396.djvu
3. Motivic Homology Theory......Page page000399.djvu
4. Stable Motivic Complexes......Page page000400.djvu
5. The Hurewicz functor......Page page000401.djvu
References......Page page000403.djvu