p-adic Analysis: Proceedings of the International Conference held in Trento, Italy, May 29–June 2, 1989

B. Dwork (auth.), Francesco Baldassarri, Siegfried Bosch, Bernard Dwork (eds.)3540534776, 9783540534778, 0387534776

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.

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Table of contents :
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