p-adic Analysis: Proceedings of the International Conference held in Trento, Italy, May 29-June 2, 1989 (Lecture Notes in Mathematics, 1454) (English and French Edition)

The International Conference on p-adic Analysis is usually held every 3-4 years with the purpose of exchanging information at research level on new trends in the subject and of reporting on progress in central problems. This particular conference, held in Trento, Italy in May 1989, was dedicated to the memory of Philippe Robba, his important contributions to p-adic analysis and especially to the theory of p-adic differential equations. The conference was characterized by the discussion of numerous algebraic geometries. Rigid cohomology, D-modules and the action of Frobenius on the cohomology of curves and abelian varieties were the central themes of several contributions. A number of talks were devoted to exponential sums, a theme connecting p-adic analysis, algebraic geometry and number theory. Other themes were p-adic moduli spaces, non-Archimedean functional analysis, Barsotti-Tate groups and Drinfeld modules. Work of Philippe Robba....Pages 1-10 p -Adic estimates for exponential sums....Pages 11-22 p-Adic Betti lattices....Pages 23-63 The nonarchimedean Banach-Stone theorem....Pages 64-79 Cohomologie rigide et théorie des D -modules....Pages 80-124 Extensions de D-modules et groupes de Galois differentiels....Pages 125-141 Duality in rigid analysis....Pages 142-172 On the Frobenius matrices of fermat curves....Pages 173-193 Supercongruences....Pages 194-204 Witt realization of the p -adic Barsotti-Tate groups; some applications....Pages 205-216 Polyedres de Newton et poids de sommes exponentielles....Pages 217-222 De rham cohomology and the Gauss-manin connection for drinfeld modules....Pages 223-255 The nonarchimedean extended Teichmüller space....Pages 256-266 Sur les coefficients de De Rham-Grothendieck des varietes algebriques....Pages 267-308 On a functional equation of igusa's local zeta function....Pages 309-313 On vanishing of cohomologies of rigid analytic spaces....Pages 314-318 A p -adic analogue of the Chowla-Selberg formula....Pages 319-341 The complementation property of l ∞ in p -adic banach spaces....Pages 342-350 Gross-Koblitz formula for function fields....Pages 351-355 Three generalizations of Mahler's expansion for continuous functions on Z p ....Pages 356-361 P -adic symmetric domains....Pages 362-378 Dedicated to Philippe Robba, this conference was characterized by the discussion of numerous algebraic geometries. Other papers were devoted to exponential sums, a theme connecting p-adic analysis to number theory. F. Baldassarri, S. Bosch, B. Dwork (eds.). Conference Organized By The Centro Internazionale Per La Ricerca Matematica, Trento, Italy. Includes Bibliographical References.