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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

MathSciNet review: 2952710
Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Kiran Kedlaya
Title: $p$-adic differential equations
Additional book information: Cambridge Studies in Advanced Mathematics, Vol. 125, Cambridge University Press, Cambridge, 2010, xviii+380 pp., ISBN 978-0-521-76879-5

References [Enhancements On Off] (What's this?)

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  • Yves André, Représentations galoisiennes et opérateurs de Bessel $p$-adiques, Ann. Inst. Fourier (Grenoble) 52 (2002), no. 3, 779–808 (French, with English and French summaries). MR 1907387
  • Bruno Chiarellotto, An invitation to $p$-adic differential equations, Arithmetic and Galois theory of differential equations, Séminaires et Congrès, vol. 23, 2011, pp. 115–168.
  • Gilles Christol and Zoghman Mebkhout, Équations différentielles $p$-adiques et coefficients $p$-adiques sur les courbes, Astérisque 279 (2002), 125–183 (French, with French summary). Cohomologies $p$-adiques et applications arithmétiques, II. MR 1922830
  • Philippe Robba and Gilles Christol, Équations différentielles $p$-adiques, Actualités Mathématiques. [Current Mathematical Topics], Hermann, Paris, 1994 (French, with French summary). Applications aux sommes exponentielles. [Applications to exponential sums]. MR 1411447
  • Bernard M. Dwork, Lectures on $p$-adic differential equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 253, Springer-Verlag, New York-Berlin, 1982. With an appendix by Alan Adolphson. MR 678093
  • Kiran S. Kedlaya, A $p$-adic local monodromy theorem, Ann. of Math. (2) 160 (2004), no. 1, 93–184. MR 2119719, DOI 10.4007/annals.2004.160.93
  • Kiran S. Kedlaya, Local monodromy of $p$-adic differential equations: an overview, Int. J. Number Theory 1 (2005), no. 1, 109–154. MR 2172335, DOI 10.1142/S179304210500008X
  • Kiran S. Kedlaya, Fourier transforms and $p$-adic ‘Weil II’, Compos. Math. 142 (2006), no. 6, 1426–1450. MR 2278753, DOI 10.1112/S0010437X06002338
  • Elisabeth Lutz, Sur l’équation $y^2=x^3-ax-b$ dans les corps $p$-adiques, J. Reine Angew. Math. (1937), no. 177, 238–243.
  • Z. Mebkhout, Analogue $p$-adique du théorème de Turrittin et le théorème de la monodromie $p$-adique, Invent. Math. 148 (2002), no. 2, 319–351 (French). MR 1906152, DOI 10.1007/s002220100208
  • Zoghman Mebkhout, La théorie des équations différentielles $p$-adiques et le théorème de la monodromie $p$-adique, Proceedings of the International Conference on Algebraic Geometry and Singularities (Spanish) (Sevilla, 2001), 2003, pp. 623–665 (French, with English summary). MR 2023201, DOI 10.4171/RMI/363
  • H. L. Turrittin, Convergent solutions of ordinary linear homogeneous differential equations in the neighborhood of an irregular singular point, Acta Math. 93 (1955), 27–66. MR 68689, DOI 10.1007/BF02392519

  • Review Information:

    Reviewer: Laurent Berger
    Affiliation: UMPA, ENS de Lyon, UMR 5669 du CNRS, Université de Lyon, France
    Journal: Bull. Amer. Math. Soc. 49 (2012), 465-468
    Published electronically: January 25, 2012
    Review copyright: © Copyright 2012 American Mathematical Society