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170329 ||| eng |
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|a 9781400837151
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|a Berkovich, Vladimir G.
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|a Integration of One-forms on P-adic Analytic Spaces. (AM-162)
|h Elektronische Ressource
|c Vladimir G. Berkovich
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| 250 |
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|a Course Book
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| 260 |
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|a Princeton, N.J.
|b Princeton University Press
|c [2007]©2007, 2007
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| 300 |
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|a online resource 168 pages
|b illustrations
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| 653 |
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|a Geometry and Topology
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| 653 |
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|a Mathematik
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| 653 |
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|a Analyse p-adique
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| 653 |
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|a MATHEMATICS / Number Theory
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| 653 |
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|a MATHEMATICS / Differential Equations / General
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|a p-adic analysis
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| 653 |
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|a Mathematics
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|a eng
|2 ISO 639-2
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| 989 |
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|b GRUYMPG
|a DeGruyter MPG Collection
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| 490 |
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|a Annals of Mathematics Studies
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| 500 |
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|a Mode of access: Internet via World Wide Web
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|a 10.1515/9781400837151
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|t Princeton eBook Package Backlist 2000-2013
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|t Princeton Univ. Press eBook Package 2000-2013
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|t Princeton eBook Package Backlist 2000-2014
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|t Princeton Annals of Mathematics Backlist eBook Package
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|u https://www.degruyter.com/doi/book/10.1515/9781400837151
|x Verlag
|3 Volltext
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|a 512.74
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|a 512.74
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|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
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