Dissertation/Thesis Abstract

Extending Oda's Theorem to Curves with Ordinary Singularities
by Taylor, J. David, Ph.D., The University of Arizona, 2020, 163; 28026225
Abstract (Summary)

We extend a result of Tadao Oda [26] (Corollary 5.11) to the case of a reduced proper curve X over a perfect field of characteristic p with at worst ordinary multiple points as singularities. Our result identifies the Dieudonné module of the finite k-group scheme Pic0 X/k[p] with a cohomological construction on X generalizing de Rham cohomology. Much of this thesis is devoted to developing relevant background material and giving a detailed review of Oda’s proof. Our method of proof uses Oda’s theorem and is not a replacement for it. However, one of our central results is an alternate characterization of Oda’s map.

Indexing (document details)
Advisor: Cais, Bryden
Commitee: Ulmer, Douglas, Xue, Hang, Levin, Brandon
School: The University of Arizona
Department: Mathematics
School Location: United States -- Arizona
Source: DAI-B 82/1(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Dieudonné theory, Logarithmic differential, Ordinary multiple points, Picard scheme, Semiabelian variety, Singular curve
Publication Number: 28026225
ISBN: 9798662470521
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