Nonarchimedean differential modules and ramification theory
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465223691-MIT.pdf
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Author(s)
Xiao, Liang, Ph. D. Massachusetts Institute of Technology
Advisor(s)
Kiran S. Kedlaya.
Date Issued
2009
Publisher
Massachusetts Institute of Technology
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009.
Includes bibliographical references (p. 253-257).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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