Integration of One-forms on P-adic Analytic Spaces. (AM-162) /

Among the many differences between classical and p-adic objects, those related to differential equations occupy a special place. For example, a closed p-adic analytic one-form defined on a simply-connected domain does not necessarily have a primitive in the class of analytic functions. In the early...

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Detalles Bibliográficos
Autor principal: Berkovich, Vladimir G.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, N.J. : Princeton University Press, 2007.
Colección:Book collections on Project MUSE.
Temas:
p-adic analysis.
MATHEMATICS > Differential Equations > General.
MATHEMATICS > Number Theory.
Analyse p-adique.
Electronic books.
Acceso en línea:Texto completo

MARC

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100 1 |a Berkovich, Vladimir G. 
245 1 0 |a Integration of One-forms on P-adic Analytic Spaces. (AM-162) /   |c Vladimir G. Berkovich. 
264 1 |a Princeton, N.J. :  |b Princeton University Press,  |c 2007. 
264 3 |a Baltimore, Md. :  |b Project MUSE,   |c 0000 
264 4 |c ©2007. 
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490 0 |a Annals of mathematics studies ;  |v no. 162 
505 0 |a Naive analytic functions and formulation of the main result -- Étale neighborhoods of a point in a smooth analytic space -- Properties of strictly poly-stable and marked formal schemes -- Properties of the sheaves -- Isocrystals -- F-isocrystals -- Construction of the Sheaves -- Properties of the sheaves -- Integration and parallel transport along a path. 
520 |a Among the many differences between classical and p-adic objects, those related to differential equations occupy a special place. For example, a closed p-adic analytic one-form defined on a simply-connected domain does not necessarily have a primitive in the class of analytic functions. In the early 1980s, Robert Coleman discovered a way to construct primitives of analytic one-forms on certain smooth p-adic analytic curves in a bigger class of functions. Since then, there have been several attempts to generalize his ideas to smooth p-adic analytic spaces of higher dimension, but the spaces considered were invariably associated with algebraic varieties. This book aims to show that every smooth p-adic analytic space is provided with a sheaf of functions that includes all analytic ones and satisfies a uniqueness property. It also contains local primitives of all closed one-forms with coefficients in the sheaf that, in the case considered by Coleman, coincide with those he constructed. In consequence, one constructs a parallel transport of local solutions of a unipotent differential equation and an integral of a closed one-form along a path so that both depend nontrivially on the homotopy class of the path. Both the author's previous results on geometric properties of smooth p-adic analytic spaces and the theory of isocrystals are further developed in this book, which is aimed at graduate students and mathematicians working in the areas of non-Archimedean analytic geometry, number theory, and algebraic geometry. 
546 |a In English. 
588 |a Description based on print version record. 
650 7 |a p-adic analysis.  |2 fast  |0 (OCoLC)fst01185026 
650 7 |a MATHEMATICS  |x Differential Equations  |x General.  |2 bisacsh 
650 7 |a MATHEMATICS  |x Number Theory.  |2 bisacsh 
650 6 |a Analyse p-adique. 
650 0 |a p-adic analysis. 
655 7 |a Electronic books.   |2 local 
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830 0 |a Book collections on Project MUSE. 
856 4 0 |z Texto completo  |u https://projectmuse.uam.elogim.com/book/33477/ 
945 |a Project MUSE - Custom Collection 

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