Degenerating abelian varieties via log abelian varieties

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.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2023

Author dc:creator

• Zhao, Heer

Advisor dc:contributor.advisor

• Scholl, Anthony

• degeneration of abelian varieties
• log abelian variety
• log geometry

Licence

• https://www.repository.cam.ac.uk/bitstreams/07fca20e-2941-4ca0-8368-5beb3a7272aa/download
• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

eng

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.109717

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/370226