Hidden Bibliographic Details
| ISBN: | 9781400837151
1400837154
0691127417
9780691127415
0691128626
9780691128627
1299133339
9781299133334
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| Notes: | Includes bibliographical references and indexes.
Restrictions unspecified
Electronic reproduction. [Place of publication not identified] : HathiTrust Digital Library, 2010.
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. http://purl.oclc.org/DLF/benchrepro0212
In English.
digitized 2010 HathiTrust Digital Library committed to preserve
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| Summary: | 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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| Other form: | Print version: Berkovich, Vladimir G. Integration of one-forms on p-adic analytic spaces. Princeton, N.J. : Princeton University Press, 2007 0691127417
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| Standard no.: | 10.1515/9781400837151
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