<I>p</I>-adic Differential Equations

Kiran S. Kedlaya

doi:10.1017/CBO9780511750922

p-adic Differential Equations

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Cited by 66
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This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

Kedlaya, Kiran S. and Tynan, Philip 2009. Detecting integral polyhedral functions . Confluentes Mathematici, Vol. 1, Issue. 1, p. 87.

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Baldassarri, Francesco 2010. Continuity of the radius of convergence of differential equations on p-adic analytic curves. Inventiones mathematicae, Vol. 182, Issue. 3, p. 513.

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Kedlaya, Kiran S. and Xiao, Liang 2010. Differential modules onp-adic polyannuli. Journal of the Institute of Mathematics of Jussieu, Vol. 9, Issue. 1, p. 155.

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Kedlaya, Kiran S. and Xiao, Liang 2010. Differential Modules on p-Adic Polyannuli—Erratum. Journal of the Institute of Mathematics of Jussieu, Vol. 9, Issue. 3, p. 669.

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Xiao, Liang 2010. On ramification filtrations andp-adic differential modules, I: the equal characteristic case. Algebra & Number Theory, Vol. 4, Issue. 8, p. 969.

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Kedlaya, Kiran 2010. Good formal structures for flat meromorphic connections, II: Excellent schemes. Journal of the American Mathematical Society, Vol. 24, Issue. 1, p. 183.

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Kedlaya, Kiran S. 2011. Swan conductors for p-adic differential modules. II Global variation. Journal of the Institute of Mathematics of Jussieu, Vol. 10, Issue. 1, p. 191.

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Abe, Tomoyuki 2011. Coherence of certain overconvergent isocrystals without Frobenius structures on curves. Mathematische Annalen, Vol. 350, Issue. 3, p. 577.

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Shiho, Atsushi 2011. Cut-by-curves criterion for the log extendability of overconvergent isocrystals. Mathematische Zeitschrift, Vol. 269, Issue. 1-2, p. 59.

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Kedlaya, Kiran S. 2011. Semistable reduction for overconvergentF-isocrystals, IV: local semistable reduction at nonmonomial valuations. Compositio Mathematica, Vol. 147, Issue. 2, p. 467.

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Lauder, Alan G. B. 2011. Degenerations and limit Frobenius structures in rigid cohomology. LMS Journal of Computation and Mathematics, Vol. 14, Issue. , p. 1.

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Xiao, Liang 2012. On the refined ramification filtrations in the equal characteristic case. Algebra & Number Theory, Vol. 6, Issue. 8, p. 1579.

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Xiao, Liang 2012. On ramification filtrations and p-adic differential equations, II: mixed characteristic case. Compositio Mathematica, Vol. 148, Issue. 2, p. 415.

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Nakagawa, Takahiro 2013. The logarithmic growth of element of Robba ring which satisfies Frobenius equation over bounded Robba ring. Tohoku Mathematical Journal, Vol. 65, Issue. 2,

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Baldassarri, Francesco 2013. Radius of Convergence of p-adic Connections and the p-adic Rolle Theorem. Milan Journal of Mathematics, Vol. 81, Issue. 2, p. 397.

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Baldassarri, Francesco 2014. RETRACTED ARTICLE: Radius of convergence of $$p$$ p -adic connections and the Berkovich ramification locus. Mathematische Annalen, Vol. 360, Issue. 3-4, p. 1109.

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Kedlaya, Kiran S. 2015. Local and global structure of connections on nonarchimedean curves. Compositio Mathematica, Vol. 151, Issue. 6, p. 1096.

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Kedlaya, Kiran S 2015. New methods for $$(\varphi, \Gamma)$$ ( φ , Γ ) -modules. Research in the Mathematical Sciences, Vol. 2, Issue. 1,

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Ohkubo, Shun 2015. On differential modules associated to de Rham representations in the imperfect residue field case. Algebra & Number Theory, Vol. 9, Issue. 8, p. 1881.

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Xiao, Liang 2015. Cleanliness and log-characteristic cycles for vector bundles with flat connections. Mathematische Annalen, Vol. 362, Issue. 1-2, p. 579.

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Kiran S. Kedlaya, Massachusetts Institute of Technology

Publisher:: Cambridge University Press
Online publication date:: August 2012
Print publication year:: 2010
Online ISBN:: 9780511750922
DOI:: https://doi.org/10.1017/CBO9780511750922

Subjects:: Mathematics (general), Mathematics, Number Theory
Series:: Cambridge Studies in Advanced Mathematics (125)

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Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study.

'Before this book appeared, it was not easy for graduate students and researchers to study p-adic differential equations and related topics because on needed to read a lot of original papers. Now one can easily access these areas via this book.'

Source: Mathematical Reviews

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p-adic Differential Equations

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