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Item Details
| Title:
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INTEGRATION OF ONE-FORMS ON P-ADIC ANALYTIC SPACES
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| By: |
Vladimir G. Berkovich |
| Format: |
Hardback |
| List price:
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£55.00 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0691127417 |
| ISBN 13: |
9780691127415 |
| Publisher: |
PRINCETON UNIVERSITY PRESS |
| Pub. date: |
13 November, 2006 |
| Series: |
Annals of Mathematics Studies No. 162 |
| Pages: |
168 |
| Description: |
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. |
| Synopsis: |
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. |
| Illustrations: |
14 line illus. |
| Publication: |
US |
| Imprint: |
Princeton University Press |
| Returns: |
Non-returnable |
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