rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: p-adic differential equations
  name:
    name part: Kedlaya, Kiran Sridhara
    name part: 1974-
    role:
      role term: creator
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: enk
    date issued: 2010
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: print
    extent: xvii, 380 pages : illustrations ; 24 cm.
  abstract: "Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study"--
  abstract: "Although the very existence of a highly developed theory of p-adic ordinary differential equations is not entirely well known even within number theory, the subject is actually almost 50 years old. Here are circumstances, past and present, in which it arises"--
  table of contents: Machine generated contents note: 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.
  note: Kiran S. Kedlaya.
  note: Includes bibliographical references and index.
  subject:
    topic: p-adic analysis
  subject:
    topic: Differential equations
  classification: QA241 .K43 2010
  classification: 512.7/4
  related item:
    title info:
      title: Cambridge studies in advanced mathematics ; 125
  identifier: 9780521768795
  identifier: 0521768799
  identifier: 2010004489
  identifier: http://www.loc.gov/catdir/enhancements/fy1006/2010004489-t.html
  identifier: http://www.loc.gov/catdir/enhancements/fy1006/2010004489-d.html
  identifier: http://www.loc.gov/catdir/enhancements/fy1006/2010004489-b.html
  related item:
    location:
      url: http://www.loc.gov/catdir/enhancements/fy1006/2010004489-t.html
  related item:
    location:
      url: http://www.loc.gov/catdir/enhancements/fy1006/2010004489-d.html
  related item:
    location:
      url: http://www.loc.gov/catdir/enhancements/fy1006/2010004489-b.html
  record info:
    record content source: DLC
    record creation date: 100201
    record change date: 20151201154721.0
    record identifier: in00002605545