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Integration of one-forms on p-adic analytic spaces /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton, N.J. :
Princeton University Press,
2007.
|
| Colección: | Annals of mathematics studies ;
no. 162. |
| Temas: | |
| 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 / |c Vladimir G. Berkovich. |
| 260 | |a Princeton, N.J. : |b Princeton University Press, |c 2007. | ||
| 300 | |a 1 online resource (vi, 156 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a Annals of mathematics studies ; |v no. 162 | |
| 504 | |a Includes bibliographical references and indexes. | ||
| 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. | |
| 506 | |3 Use copy |f Restrictions unspecified |2 star |5 MiAaHDL | ||
| 533 | |a Electronic reproduction. |b [Place of publication not identified] : |c HathiTrust Digital Library, |d 2010. |5 MiAaHDL | ||
| 538 | |a Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |u http://purl.oclc.org/DLF/benchrepro0212 |5 MiAaHDL | ||
| 583 | 1 | |a digitized |c 2010 |h HathiTrust Digital Library |l committed to preserve |2 pda |5 MiAaHDL | |
| 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. | ||
| 590 | |a JSTOR |b Books at JSTOR All Purchased | ||
| 590 | |a JSTOR |b Books at JSTOR Evidence Based Acquisitions | ||
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
| 650 | 0 | |a p-adic analysis. | |
| 650 | 6 | |a Analyse p-adique. | |
| 650 | 7 | |a MATHEMATICS |x Number Theory. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x General. |2 bisacsh | |
| 650 | 7 | |a p-adic analysis. |2 fast |0 (OCoLC)fst01185026 | |
| 776 | 0 | 8 | |i Print version: |a Berkovich, Vladimir G. |t Integration of one-forms on p-adic analytic spaces. |d Princeton, N.J. : Princeton University Press, 2007 |z 0691127417 |w (DLC) 2006921278 |w (OCoLC)73955249 |
| 830 | 0 | |a Annals of mathematics studies ; |v no. 162. | |
| 856 | 4 | 0 | |u https://jstor.uam.elogim.com/stable/10.2307/j.ctt24hrs9 |z Texto completo |
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