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Degenerating abelian varieties via log abelian varieties https://doi.org/10.17863/CAM.109717 Zhao, Heer Scholl, Anthony 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. University of Cambridge 2023-12-22 Thesis Doctoral Doctor of Philosophy (PhD) eng 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). https://www.repository.cam.ac.uk/handle/1810/370226 https://www.repository.cam.ac.uk/bitstreams/2d503955-3915-4039-be5b-54b85fb06de9/download 93660e2f468e4b535484e034199e2339 https://www.repository.cam.ac.uk/bitstreams/07fca20e-2941-4ca0-8368-5beb3a7272aa/download 87eda9de84448d1f82354d60eee3eb5f https://www.rioxx.net/licenses/all-rights-reserved/ degeneration of abelian varieties log abelian variety log geometry