Topological automorphic forms / / Mark Behrens, Tyler Lawson

• Autore: Behrens Mark <1975->
• Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , 2009; ©2009
• Descrizione fisica: 1 online resource (167 p.)
• Disciplina: 515.9
• Soggetto topico: Automorphic forms; Algebraic topology; Homotopy groups; Shimura varieties
• Persona (resp. second.): LawsonTyler <1977->
• Note generali: "Volume 204, Number 958 (second of 5 numbers)."
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: ""Contents""; ""Abstract""; ""Introduction""; ""0.1. Background and motivation""; ""0.2. Subject matter of this book""; ""0.3. Organization of this book""; ""0.4. Acknowledgments""; ""Chapter 1. p-divisible groups""; ""1.1. Definitions""; ""1.2. Classification""; ""Chapter 2. The Honda-Tate classification""; ""2.1. Abelian varieties over finite fields""; ""2.2. Abelian varieties over Fp""; ""Chapter 3. Tate modules and level structures""; ""3.1. Tate modules of abelian varieties""; ""3.2. Virtual subgroups and quasi-isogenies""; ""3.3. Level structures""; ""3.4. The Tate representation"" ; ""3.5. Homomorphisms of abelian schemes""""Chapter 4. Polarizations""; ""4.1. Polarizations""; ""4.2. The Rosati involution""; ""4.3. The Weil pairing""; ""4.4. Polarizations of B-linear abelian varieties""; ""4.5. Induced polarizations""; ""4.6. Classification of weak polarizations""; ""Chapter 5. Forms and involutions""; ""5.1. Hermitian forms""; ""5.2. Unitary and similitude groups""; ""5.3. Classification of forms""; ""Chapter 6. Shimura varieties of type U(1,n-1)""; ""6.1. Motivation""; ""6.2. Initial data""; ""6.3. Statement of the moduli problem"" ; ""6.4. Equivalence of the moduli problems""""6.5. Moduli problems with level structure""; ""6.6. Shimura stacks""; ""Chapter 7. Deformation theory""; ""7.1. Deformations of p-divisible groups""; ""7.2. Serre-Tate theory""; ""7.3. Deformation theory of points of Sh""; ""Chapter 8. Topological automorphic forms""; ""8.1. The generalized Hopkins-Miller theorem""; ""8.2. The descent spectral sequence""; ""8.3. Application to Shimura stacks""; ""Chapter 9. Relationship to automorphic forms""; ""9.1. Alternate description of Sh(Kp)""; ""9.2. Description of Sh(Kp)F""; ""9.3. Description of Sh(Kp)C"" ; ""9.4. Automorphic forms""""Chapter 10. Smooth G-spectra""; ""10.1. Smooth G-sets""; ""10.2. The category of simplicial smooth G-sets""; ""10.3. The category of smooth G-spectra""; ""10.4. Smooth homotopy fixed points""; ""10.5. Restriction, induction, and coinduction""; ""10.6. Descent from compact open subgroups""; ""10.7. Transfer maps and the Burnside category""; ""Chapter 11. Operations on TAF""; ""11.1. The E-action of GU(Ap,)""; ""11.2. Hecke operators""; ""Chapter 12. Buildings""; ""12.1. Terminology""; ""12.2. The buildings for GL and SL""; ""12.3. The buildings for U and GU"" ; ""Chapter 13. Hypercohomology of adele groups""""13.1. Definition of QGU and QU""; ""13.2. The semi-cosimplicial resolution""; ""Chapter 14. K(n)-local theory""; ""14.1. Endomorphisms of mod p points""; ""14.2. Approximation results""; ""14.3. The height n locus of Sh(Kp)""; ""14.4. K(n)-local TAF""; ""14.5. K(n)-local QU""; ""Chapter 15. Example: chromatic level 1""; ""15.1. Unit groups and the K(1)-local sphere""; ""15.2. Topological automorphic forms in chromatic filtration 1""; ""Bibliography""; ""Index""
• Titolo autorizzato: Topological automorphic forms
• ISBN: 1-4704-0572-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910788857303321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society ; ; Volume 204, Number 958.