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Book Review

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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?)

  • 1. Yves André, Filtrations de type Hasse-Arf et monodromie $ p$-adique, Invent. Math. 148 (2002), no. 2, 285-317. MR 1906151 (2003k:12011)
  • 2. -, Représentations galoisiennes et opérateurs de Bessel $ p$-adiques, Ann. Inst. Fourier (Grenoble) 52 (2002), no. 3, 779-808. MR 1907387 (2003c:12010)
  • 3. 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.
  • 4. Gilles Christol and Zoghman Mebkhout, Équations différentielles $ p$-adiques et coefficients $ p$-adiques sur les courbes, Astérisque (2002), no. 279, 125-183, Cohomologies $ p$-adiques et applications arithmétiques, II. MR 1922830 (2003i:12014)
  • 5. Gilles Christol and Philippe Robba, Équations différentielles $ p$-adiques, Actualités Mathématiques. [Current Mathematical Topics], Hermann, Paris, 1994, Applications aux sommes exponentielles. [Applications to exponential sums]. MR 1411447 (97g:12005)
  • 6. Bernard M. Dwork, Lectures on $ p$-adic differential equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 253, Springer-Verlag, New York, 1982, With an appendix by Alan Adolphson. MR 678093 (84g:12031)
  • 7. Kiran S. Kedlaya, A $ p$-adic local monodromy theorem, Ann. of Math. (2) 160 (2004), no. 1, 93-184. MR 2119719 (2005k:14038)
  • 8. -, Local monodromy of $ p$-adic differential equations: an overview, Int. J. Number Theory 1 (2005), no. 1, 109-154. MR 2172335 (2006g:12013)
  • 9. -, Fourier transforms and $ p$-adic `Weil II', Compos. Math. 142 (2006), no. 6, 1426-1450. MR 2278753 (2008b:14024)
  • 10. 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.
  • 11. Zoghman Mebkhout, Analogue $ p$-adique du théorème de Turrittin et le théorème de la monodromie $ p$-adique, Invent. Math. 148 (2002), no. 2, 319-351. MR 1906152 (2003k:14018)
  • 12. -, 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), vol. 19, 2003, pp. 623-665. MR 2023201 (2005a:12012)
  • 13. Hugh 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 0068689 (16,925a)

Review Information:

Reviewer: Laurent Berger
Affiliation: UMPA, ENS de Lyon, UMR 5669 du CNRS Université de Lyon, France
Email: laurent.berger@ens-lyon.fr
Journal: Bull. Amer. Math. Soc. 49 (2012), 465-468
MSC (2010): Primary 12H25
DOI: https://doi.org/10.1090/S0273-0979-2012-01371-X
Published electronically: January 25, 2012
Review copyright: © Copyright 2012 American Mathematical Society
American Mathematical Society