Degenerating abelian varieties via log abelian varieties
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Authors
Zhao, Heer
Abstract
This thesis is based on the author's paper [52]. It extends the construction of log Tate curves from [25, §1] to higher dimensions. The approach involves extensive applications of algebraic spaces and higher-dimensional convex geometry to create diverse models for any given split totally degenerate semi-stable abelian variety over a complete discrete valuation field. Such models are used to construct a log abelian variety over the corresponding discrete valuation ring (endowed with the canonical log structure), which extends the given abelian variety.
Description
Date
2023-12-22
Advisors
Scholl, Anthony
Keywords
degeneration of abelian varieties, log abelian variety, log geometry
Qualification
Doctor of Philosophy (PhD)
Awarding Institution
University of Cambridge
Rights
Sponsorship
The Cambridge Overseas Trust (covering the University Composition Fee at the home rate, College Fee, and Maintenance Allowance)
The Department of Pure Mathematics and Mathematical Statistics (bridging the difference between the home rate and the international rate for the University Composition Fee).