p-adic differential equations

p-adic differential equations

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Détails bibliographiques
Auteur principal : Kedlaya Kiran Sridhara (Auteur)
Format : Livre
Langue : anglais
Titre complet : p-adic differential equations / Kiran S. Kedlaya,...
Publié : Cambridge, New York, Melbourne [etc.] : Cambridge University Press , cop. 2010
Description matérielle : 1 vol. (XVII-380 p.)
Collection : Cambridge studies in advanced mathematics ; 125
Accès en ligne : Lien vers la préface et la table des matières
Sujets :
Analyse p-adique
Équations différentielles
  • 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 differential algebra
  • 6. Metric properties of differential modules
  • 7. Regular singularities
  • Part III. p-adic Differential Equations on Discs and Annuli
  • 8. Rings of functions on discs and annuli
  • 9. Radius and generic radius of convergence
  • 10. Frobenius pullback and pushforward
  • 11. Variation of generic and subsidiary radii
  • 12. Decomposition by subsidiary radii
  • 13. p-adic exponents
  • Part IV. Difference Algebra and Frobenius Modules
  • 14. Formalism of difference algebra
  • 15. Frobenius modules
  • 16. Frobenius modules over the Robba ring
  • Part V. Frobenius Structures
  • 17. Frobenius structures on differential modules
  • 18. Effective convergence bounds
  • 19. Galois representations and differential modules
  • 20. The p-adic local monodromy theorem: 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