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Book review of: K. S. Kedlaya, \(p\)-adic differential equations. (English) Zbl 1300.00010

Review of [Zbl 1213.12009].

MSC:

00A17 External book reviews
12-02 Research exposition (monographs, survey articles) pertaining to field theory
12H25 \(p\)-adic differential equations
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
12H05 Differential algebra
14G20 Local ground fields in algebraic geometry
13A35 Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure

Citations:

Zbl 1213.12009
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Full Text: DOI

References:

[1] Yves André, Filtrations de type Hasse-Arf et monodromie \?-adique, Invent. Math. 148 (2002), no. 2, 285 – 317 (French). · Zbl 1081.12003 · doi:10.1007/s002220100207
[2] Yves André, Représentations galoisiennes et opérateurs de Bessel \?-adiques, Ann. Inst. Fourier (Grenoble) 52 (2002), no. 3, 779 – 808 (French, with English and French summaries). · Zbl 1014.12007
[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. · Zbl 1356.12009
[4] Gilles Christol and Zoghman Mebkhout, Équations différentielles \?-adiques et coefficients \?-adiques sur les courbes, Astérisque 279 (2002), 125 – 183 (French, with French summary). Cohomologies \?-adiques et applications arithmétiques, II. · Zbl 1031.12004
[5] Philippe Robba and Gilles Christol, Équations différentielles \?-adiques, Actualités Mathématiques. [Current Mathematical Topics], Hermann, Paris, 1994 (French, with French summary). Applications aux sommes exponentielles. [Applications to exponential sums]. · Zbl 0868.12006
[6] Bernard M. Dwork, Lectures on \?-adic differential equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 253, Springer-Verlag, New York-Berlin, 1982. With an appendix by Alan Adolphson. · Zbl 0502.12021
[7] Kiran S. Kedlaya, A \?-adic local monodromy theorem, Ann. of Math. (2) 160 (2004), no. 1, 93 – 184. · Zbl 1088.14005 · doi:10.4007/annals.2004.160.93
[8] Kiran S. Kedlaya, Local monodromy of \?-adic differential equations: an overview, Int. J. Number Theory 1 (2005), no. 1, 109 – 154. · Zbl 1107.12005 · doi:10.1142/S179304210500008X
[9] Kiran S. Kedlaya, Fourier transforms and \?-adic ’Weil II’, Compos. Math. 142 (2006), no. 6, 1426 – 1450. · Zbl 1119.14014 · doi:10.1112/S0010437X06002338
[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. · Zbl 0017.05307
[11] Z. Mebkhout, Analogue \?-adique du théorème de Turrittin et le théorème de la monodromie \?-adique, Invent. Math. 148 (2002), no. 2, 319 – 351 (French). · Zbl 1071.12004 · doi:10.1007/s002220100208
[12] Zoghman Mebkhout, La théorie des équations différentielles \?-adiques et le théorème de la monodromie \?-adique, Proceedings of the International Conference on Algebraic Geometry and Singularities (Spanish) (Sevilla, 2001), 2003, pp. 623 – 665 (French, with English summary). · Zbl 1113.12004 · doi: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. · Zbl 0064.33603 · doi:10.1007/BF02392519
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