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Nonarchimedean differential modules and ramification theory

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dc.contributor.advisor Kiran S. Kedlaya. en_US Xiao, Liang, Ph. D. Massachusetts Institute of Technology en_US
dc.contributor.other Massachusetts Institute of Technology. Dept. of Mathematics. en_US 2010-01-07T20:58:32Z 2010-01-07T20:58:32Z 2009 en_US 2009 en_US
dc.description Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009. en_US
dc.description Includes bibliographical references (p. 253-257). en_US
dc.description.abstract In this thesis, I first systematically develop the theory of nonarchimedean differential modules, deducing fundamental theorems about the variation of generic radii of convergence for differential modules over polyannuli. The theorems assert that the log of subsidiary radii of convergence are convex, continuous, and piecewise affine functions of the log of the radii of the polyannuli. Then I apply these results to the ramification theory and deduce the fundamental result, Hasse-Arf theorem, for ramification filtrations defined by Abbes and Saito. Also, we include a comparison theorem to differential conductors and Borger's conductors in the equal characteristic case. Finally, I globalize this construction and give a new understanding of the ramification theory for smooth varieties, which provides some new insight to the global class field theory. We end the thesis with a series of conjectures as a starting point of a long going project on understanding global ramification. en_US
dc.description.statementofresponsibility by Liang Xiao. en_US
dc.format.extent 257 p. en_US
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.rights.uri en_US
dc.subject Mathematics. en_US
dc.title Nonarchimedean differential modules and ramification theory en_US
dc.type Thesis en_US Ph.D. en_US
dc.contributor.department Massachusetts Institute of Technology. Dept. of Mathematics. en_US
dc.identifier.oclc 465223691 en_US

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