Title 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

Published Providence, Rhode Island : American Mathematical Society, [1987] ©1987

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Description 1 online resource (311 pages) : illustrations Series Contemporary mathematics, 0271-4132 ; volume 67 Contemporary mathematics (American Mathematical Society) ; volume 67. Contents ""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""; ""Â1. Endomorphisms of the additive group""; ""Â2. Definition of Drinfei 'd module over a field""; ""Â3. Division points""; ""Â4. Isogenies"" ""Â5. Drinfel 'd modules over a base scheme""""Â6. Level structure and the moduli space""; ""Chapter 2. Analytic theory of the affine modules of Drinfel 'd""; ""Â1. Exponential function associated to a lattice""; ""Â2. Characterization of Drinfel 'd modules over Câe17E;""; ""Â3. Discrete modules in a vector space over a local field""; ""Â4. Moduli spaces as homogeneous spaces (local theory)""; ""Â5. Moduli spaces as homogeneous spaces (adelic theory)""; ""Chapter 3. The rigid analytic moduli space""; ""Â1. Norms on vector spaces over a local field"" ""Â2. The building for PGL(V) over a local field""""Â3. Metric on the building""; ""Â4. The mapping from the p-adic symmetric space to the building""; ""Â5. Filtration of the I-dimensional p-adic symmetric space""; ""Chapter 4. Cohomology of the moduli space""; ""Â1. Generalities of the cohomology of rigid analytic spaces""; ""Â2. Cohomology of Ω2 (C17E;)""; ""Â3. A simple topological model""; ""Â4. 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 Notes 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"--Title page verso Bibliography Includes bibliographical references Notes English Print version record Subject Arithmetical algebraic geometry -- Congresses Arithmetical algebraic geometry Genre/Form Conference papers and proceedings Form Electronic book Author Ribet, Kenneth, editor ISBN 9780821833858 0821833855

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