Lectures on p-adic differential equations. (English) Zbl 0502.12021

Dwork, Bernard

Grundlehren der Mathematischen Wissenschaften, 253. New York Heidelberg - Berlin: Springer-Verlag. VIII, 310 p. DM 118.00; $ 47.20 (1982).

MSC:

12H25	\(p\)-adic differential equations
12-02	Research exposition (monographs, survey articles) pertaining to field theory
14-02	Research exposition (monographs, survey articles) pertaining to algebraic geometry
34-02	Research exposition (monographs, survey articles) pertaining to ordinary differential equations
14G20	Local ground fields in algebraic geometry
34G10	Linear differential equations in abstract spaces
14F30	\(p\)-adic cohomology, crystalline cohomology
14D05	Structure of families (Picard-Lefschetz, monodromy, etc.)
14K15	Arithmetic ground fields for abelian varieties
14G10	Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
35A30	Geometric theory, characteristics, transformations in context of PDEs
14H25	Arithmetic ground fields for curves
11S80	Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)

Keywords:

linear p-adic differential equations; Picard-Fuchs equations; Gauss hypergeometric equations; strong Frobenius structure; Frobenius automorphism; Frobenius transformation; eigenvectors; normalized solution matrix; ordinary residue classes; supersingular residue classes; excellent lifting of Frobenius; Hodge filtration; growth filtration of solution space; p-adic gamma functions; beta functions; calculation of lowest degree terms in power series expansion; p-adic cohomology of algebraic curves; research suggestions in p-adic analysis

Citations:

Zbl 0219.14014; Zbl 0284.14008