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  3. p-adic Differential Equations
  • Cited by 3
      • 2nd edition
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    • Publisher:
      Cambridge University Press
      Publication date:
      August 2022
      June 2022
      ISBN:
      9781009127684
      9781009123341
      DOI:
      https://doi.org/10.1017/9781009127684
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.91kg, 518 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Number Theory
      Series:
      Cambridge Studies in Advanced Mathematics (199)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Number Theory
    Series:
    Cambridge Studies in Advanced Mathematics (199)
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    Book description

    Now in its second edition, this volume provides a uniquely detailed study of $P$-adic differential equations. Assuming only a graduate-level background in number theory, the text builds the theory from first principles all the way to the frontiers of current research, highlighting analogies and links with the classical theory of ordinary differential equations. The author includes many original results which play a key role in the study of $P$-adic geometry, crystalline cohomology, $P$-adic Hodge theory, perfectoid spaces, and algorithms for L-functions of arithmetic varieties. This updated edition contains five new chapters, which revisit the theory of convergence of solutions of $P$-adic differential equations from a more global viewpoint, introducing the Berkovich analytification of the projective line, defining convergence polygons as functions on the projective line, and deriving a global index theorem in terms of the Laplacian of the convergence polygon.

    Reviews

    ‘… the book under review is unique in the sense that it can serve as a comprehensive introduction to the subject (the monograph assumes just a graduate-level background in algebraic number theory) and as a roadmap for researchers in the area.’

    Alexander B. Levin Source: MathSciNet

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    Contents

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    Contents

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