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p-adic differential equations

Kedlaya, Kiran Sridhara, (1974-)

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p-adic differential equations

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	p-adic differential equations/ Kiran S. Kedlaya.
作者:	Kedlaya, Kiran Sridhara,
出版者:	Cambridge :Cambridge University Press, : 2010.,
面頁冊數:	xvii, 380 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
內容註:	Norms on algebraic structures -- Newton polygons -- Ramification theory -- Matrix analysis -- Formalism of differential algebra -- Metric properties of differential modules -- Regular singularities -- Rings of functions on discs and annuli -- Radius and generic radius of convergence -- Frobenius pullback and pushforward -- Variation of generic and subsidiary radii -- Decomposition by subsidiary radii -- p-adic exponents -- Formalism of difference algebra -- Frobenius modules -- Frobenius modules over the Robba ring -- Frobenius structures on differential modules -- Effective convergence bounds -- Galois representations and differential modules -- The p-adic local monodromy theorem -- The p-adic local monodromy theorem: proof -- Picard-Fuchs modules -- Rigid cohomology -- p-adic Hodge theory.
標題:	p-adic analysis. -
電子資源:	https://doi.org/10.1017/CBO9780511750922
ISBN:	9780511750922

p-adic differential equations
Kedlaya, Kiran Sridhara,1974-

p-adic differential equations[electronic resource] /Kiran S. Kedlaya. - Cambridge :Cambridge University Press,2010. - xvii, 380 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;125. - Cambridge studies in advanced mathematics ;125..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Norms on algebraic structures -- Newton polygons -- Ramification theory -- Matrix analysis -- Formalism of differential algebra -- Metric properties of differential modules -- Regular singularities -- Rings of functions on discs and annuli -- Radius and generic radius of convergence -- Frobenius pullback and pushforward -- Variation of generic and subsidiary radii -- Decomposition by subsidiary radii -- p-adic exponents -- Formalism of difference algebra -- Frobenius modules -- Frobenius modules over the Robba ring -- Frobenius structures on differential modules -- Effective convergence bounds -- Galois representations and differential modules -- The p-adic local monodromy theorem -- The p-adic local monodromy theorem: proof -- Picard-Fuchs modules -- Rigid cohomology -- p-adic Hodge theory.

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.

ISBN: 9780511750922Subjects--Topical Terms:

628821
p-adic analysis.

LC Class. No.: QA241 / .K43 2010

Dewey Class. No.: 512.74

p-adic differential equations
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a Norms on algebraic structures -- Newton polygons -- Ramification theory -- Matrix analysis -- Formalism of differential algebra -- Metric properties of differential modules -- Regular singularities -- Rings of functions on discs and annuli -- Radius and generic radius of convergence -- Frobenius pullback and pushforward -- Variation of generic and subsidiary radii -- Decomposition by subsidiary radii -- p-adic exponents -- Formalism of difference algebra -- Frobenius modules -- Frobenius modules over the Robba ring -- Frobenius structures on differential modules -- Effective convergence bounds -- Galois representations and differential modules -- The p-adic local monodromy theorem -- The p-adic local monodromy theorem: proof -- Picard-Fuchs modules -- Rigid cohomology -- p-adic Hodge theory.
520 $a 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.
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