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Degenerating abelian varieties via log abelian varieties


Type

Thesis

Change log

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
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).