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 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 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
References
- Yves André, Filtrations de type Hasse-Arf et monodromie $p$-adique, Invent. Math. 148 (2002), no. 2, 285–317. MR 1906151 (2003k:12011)
- —, Représentations galoisiennes et opérateurs de Bessel $p$-adiques, Ann. Inst. Fourier (Grenoble) 52 (2002), no. 3, 779–808. MR 1907387 (2003c:12010)
- 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 (2002), no. 279, 125–183, Cohomologies $p$-adiques et applications arithmétiques, II. MR 1922830 (2003i:12014)
- 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)
- 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)
- Kiran S. Kedlaya, A $p$-adic local monodromy theorem, Ann. of Math. (2) 160 (2004), no. 1, 93–184. MR 2119719 (2005k:14038)
- —, Local monodromy of $p$-adic differential equations: an overview, Int. J. Number Theory 1 (2005), no. 1, 109–154. MR 2172335 (2006g:12013)
- —, Fourier transforms and $p$-adic ‘Weil II’, Compos. Math. 142 (2006), no. 6, 1426–1450. MR 2278753 (2008b:14024)
- 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.
- 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)
- —, 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)
- 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
DOI:
https://doi.org/10.1090/S0273-0979-2012-01371-X
Published electronically:
January 25, 2012
Review copyright:
© Copyright 2012
American Mathematical Society
