Current trends in arithmetical algebraic geometry : proceedings of the AMS-IMS-SIAM Joint Summer Research Conference, held August 18-24, 1985, with support from the National Science Foundation / / Kenneth A. Ribet, editor

• Record Nr.: UNISA996320720503316
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , [1987]; ©1987
• ISBN: 0-8218-3385-5
• Descrizione fisica: 1 online resource (311 p.)
• Collana: Contemporary mathematics, , 0271-4132 ; ; 67 , 0271-4132
• Disciplina: 516.3/5
• Soggetti: Arithmetical algebraic geometry
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: English and French.; "AMS-IMS-SIAM Joint Summer Research Conference in the Mathematical Sciences on Current Trends in Arithmetical Algebraic Geometry was held at Humboldt State University"--T.p. verso.
• Nota di bibliografia: Includes bibliographies.
• Nota di contenuto: Contents -- Introduction -- Height pairing between algebraic cycles -- Introduction -- 1. Height pairing in geometric situation (global construction) -- 2. Local indexes over non-archimedean places -- 3. Local indexes over C or R -- 4. Height pairing over number fields -- 5. Some conjectures and problems -- Survey of Drinfel'd modules -- Introduction -- Chapter 1. Algebraic theory of Drinfel 'd modules -- 1. Endomorphisms of the additive group -- 2. Definition of Drinfei 'd module over a field -- 3. Division points -- 4. Isogenies -- 5. Drinfel 'd modules over a base scheme -- 6. Level structure and the moduli space -- Chapter 2. Analytic theory of the affine modules of Drinfel 'd -- 1. Exponential function associated to a lattice -- 2. Characterization of Drinfel 'd modules over Ce17E -- 3. Discrete modules in a vector space over a local field -- 4. Moduli spaces as homogeneous spaces (local theory) -- 5. Moduli spaces as homogeneous spaces (adelic theory) -- Chapter 3. The rigid analytic moduli space -- 1. Norms on vector spaces over a local field -- 2. The building for PGL(V) over a local field -- 3. Metric on the building -- 4. The mapping from the p-adic symmetric space to the building -- 5. ; Filtration of the I-dimensional p-adic symmetric space -- Chapter 4. Cohomology of the moduli space -- 1. Generalities of the cohomology of rigid analytic spaces -- 2. Cohomology of Î*2 (C17E --) -- 3. A simple topological model -- 4. Cohomology of the moduli space with fixed level structure -- Chapter 5. Applications to relations between automorphic forms and Galois representations -- 8. Integrale d 'un produit de premieres classes de Chern. cas general (esquisse) -- 9. IC2 et iscmorphisme de Riemann-Roch -- 10. Metriser IC2 -- 11. Le theoreme -- p-adic periods and p-adic etale cohomology -- An introduction to higher dimensional Arakelov theory -- Diophantine problems in complex hyperbolic analysis -- Cubic exponential sums and Galois representations -- Lettre -- J-F. Mestre -- A survey of the theory of height functions -- 1. Weil heights -- 2. Metrized line bundles -- 3. The degree of a metrtzed line bundle -- 4. The modular height of an abelian variety -- 5. Canonical heights on abelian varieties -- 6. The difference of the Well and canonical heights -- 7. Lower bounds for the canonical height -- 8. Specialization theorems -- Presentation De La Theorie D'Araicelov.