内容

目次

Preface; Introductory remarks; Part I. Tools of p-adic Analysis: 1.Norms on algebraic structures; 2. Newton polygons; 3. Ramification theory; 4.Matrix analysis; Part II. Differential Algebra: 5. Formalism of differentialalgebra; 6. Metric properties of differential modules; 7. Regularsingularities; Part III. p-adic Differential Equations on Discs and Annuli:8. Rings of functions on discs and annuli; 9. Radius and generic radius ofconvergence; 10. Frobenius pullback and pushforward; 11. Variation of genericand subsidiary radii; 12. Decomposition by subsidiary radii; 13. p-adicexponents; Part IV. Difference Algebra and Frobenius Modules: 14. Formalismof difference algebra; 15. Frobenius modules; 16. Frobenius modules over theRobba ring; Part V. Frobenius Structures: 17. Frobenius structures ondifferential modules; 18. Effective convergence bounds; 19. Galoisrepresentations and differential modules; 20. The p-adic local monodromytheorem: Statement; 21. The p-adic local monodromy theorem: Proof; Part VI.Areas of Application: 22. Picard-Fuchs modules; 23. Rigid cohomology; 24.p-adic Hodge theory; References; Index of notation; Index.