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...
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Princeton, N.J. :
Princeton University Press,
2007.
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| Series: | Annals of mathematics studies ;
no. 162. |
| Subjects: | |
| Online Access: | CONNECT CONNECT |
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) | ||
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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. | |
| 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. | ||
| 500 | |a EBSCO eBook Academic Comprehensive Collection North America |5 TMurS | ||
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| 650 | 0 | |a p-adic analysis. | |
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| 830 | 0 | |a Annals of mathematics studies ; |v no. 162. | |
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