Regular singular stratified bundles in positive characteristic

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A notion of regular singularity for stratified bundles on a smooth variety over an algebraically closed field of positive characteristic is introduced and studied. Special emphasis is put on the relation of such objects with the étale fundamental group of the variety.

A major result of this thesis is that a stratified bundle is regular singular with finite monodromy if and only if it is trivialized on a finite tame étale covering. This theorem provides a precise link between regular singular differential equations and tame ramification.

It is also studied in which sense the (tame) étale fundamental group controls the category of regular singular stratified bundles. Conjecturally, if the tame étale fundamental group is trivial, then so is the category of regular singular stratified bundles. Partial results in this direction are proved in the final chapter of this thesis.

Four appendices collecting background information are included for the reader's convenience.
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Dokumententyp:
Wissenschaftliche Abschlussarbeiten » Dissertation
Fakultät / Institut:
Fakultät für Mathematik
Dewey Dezimal-Klassifikation:
500 Naturwissenschaften und Mathematik » 510 Mathematik » 512 Algebra
500 Naturwissenschaften und Mathematik » 510 Mathematik » 516 Geometrie
Beitragende:
Prof. Dr. Esnault, Hélène [Betreuer(in), Doktorvater]
Prof. Dr. Phung, Ho-Hai [Gutachter(in), Rezensent(in)]
Prof. Dr. Beilinson, Alexander A. [Gutachter(in), Rezensent(in)]
Sprache:
Englisch
Kollektion / Status:
Dissertationen / Dokument veröffentlicht
Datum der Promotion:
06.07.2012
Dokument erstellt am:
19.12.2012
Promotionsantrag am:
30.05.2012
Dateien geändert am:
19.12.2012
Medientyp:
Text