Nonarchimedean differential modules and ramification theory
Author(s)Xiao, Liang, Ph. D. Massachusetts Institute of Technology
Massachusetts Institute of Technology. Dept. of Mathematics.
Kiran S. Kedlaya.
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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.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009.Includes bibliographical references (p. 253-257).
DepartmentMassachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology