Current Trends in Arithmetical Algebraic Geometry.

Intro -- 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 C∞ -- 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 (adèlic 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 Ω2 (C∞) -- 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 -- 1. Coclosed I-cochains and the special representation -- 2. Limit cohomology and automorphic forms -- 3. Properties of the correspondence π → σ(π) -- 4. Local Langlands' conjecture in characteristic p -- Bibliography.

Le déterminant de la cohomologie -- 1. Description du théorème principal -- 2. Programme -- 3. Analogies -- 4. Objets virtuels -- 5. Fibrés métriques virtuels -- 6. Integrale d'un produit de premières classes de Chern -- 7. &lt -- L , M&gt -- et cohamologie -- 8. Intégrale d 'un produit de premieres classes de Chern. cas général (esquisse) -- 9. IC2 et iscmorphisme de Riemann-Roch -- 10. Métriser IC2 -- 11. Le théorème -- p-adic periods and p-adic étale cohomology -- An introduction to higher dimensional Arakelov theory -- Diophantine problems in complex hyperbolic analysis -- Cubic exponential sums and Galois representations -- Lettre à 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 -- Présentation de la théorie d 'Arakélov.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.