{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/50596"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/50596","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Nonarchimedean differential modules and ramification theory","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Xiao, Liang, Ph. D. Massachusetts Institute of Technology"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Mathematics.","school":null,"contributors":[],"advisors":["Kiran S. Kedlaya."],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009","date_published":"2009","updated_at":"2026-07-22T22:22:00Z","subjects":["Mathematics."],"languages":["eng"],"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."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/50596","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Kiran S. Kedlaya."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. 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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."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1721.1/50596"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009.","Includes bibliographical references (p. 253-257)."]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["Nonarchimedean differential modules and ramification theory"]}]}],"canonical_facts":{"dc:contributor.advisor":["Kiran S. Kedlaya."],"dc:contributor.department":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:contributor.other":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:creator":["Xiao, Liang, Ph. D. Massachusetts Institute of Technology"],"dc:date.accessioned":["2010-01-07T20:58:32Z"],"dc:date.available":["2010-01-07T20:58:32Z"],"dc:date.issued":["2009"],"dc:description":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009.","Includes bibliographical references (p. 253-257)."],"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. 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