Book Review
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MathSciNet review: 2952710
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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
- Yves André, Filtrations de type Hasse-Arf et monodromie $p$-adique, Invent. Math. 148 (2002), no. 2, 285–317 (French). MR 1906151, DOI https://doi.org/10.1007/s002220100207
- 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 https://doi.org/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 https://doi.org/10.1142/S179304210500008X
- Kiran S. Kedlaya, Fourier transforms and $p$-adic ‘Weil II’, Compos. Math. 142 (2006), no. 6, 1426–1450. MR 2278753, DOI https://doi.org/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 https://doi.org/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 https://doi.org/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 https://doi.org/10.1007/BF02392519
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
DOI: https://doi.org/10.1090/S0273-0979-2012-01371-X
Published electronically: January 25, 2012
Review copyright: © Copyright 2012 American Mathematical Society
