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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,
Cambridge University Press,
Cambridge,
Vol. 125, 2010, xviii+380 pp., ISBN 978-0-521-76879-5.
References
- 1.
Yves
André, Filtrations de type Hasse-Arf et monodromie
𝑝-adique, Invent. Math. 148 (2002),
no. 2, 285–317 (French). MR 1906151
(2003k:12011), http://dx.doi.org/10.1007/s002220100207
- 2.
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
(2003c:12010)
- 3.
Bruno Chiarellotto, An invitation to
 -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
279 (2002), 125–183 (French, with French summary).
Cohomologies 𝑝-adiques et applications arithmétiques, II. MR 1922830
(2003i:12014)
- 5.
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 (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), http://dx.doi.org/10.4007/annals.2004.160.93
- 8.
Kiran
S. Kedlaya, Local monodromy of 𝑝-adic differential
equations: an overview, Int. J. Number Theory 1
(2005), no. 1, 109–154. MR 2172335
(2006g:12013), http://dx.doi.org/10.1142/S179304210500008X
- 9.
Kiran
S. Kedlaya, Fourier transforms and 𝑝-adic ‘Weil
II’, Compos. Math. 142 (2006), no. 6,
1426–1450. MR 2278753
(2008b:14024), http://dx.doi.org/10.1112/S0010437X06002338
- 10.
Elisabeth Lutz, Sur l'équation
 dans les corps  -adiques, J. Reine Angew. Math. (1937), no. 177, 238-243.
- 11.
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
(2003k:14018), http://dx.doi.org/10.1007/s002220100208
- 12.
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
(2005a:12012), http://dx.doi.org/10.4171/RMI/363
- 13.
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 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:
http://dx.doi.org/10.1090/S0273-0979-2012-01371-X
PII:
S 0273-0979(2012)01371-X
Posted:
January 25, 2012
Review copyright:
© Copyright 2012 American Mathematical Society
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