Asian Journal of Mathematics

Volume 22 (2018)

Number 5

Degenerating abelian varieties via log abelian varieties

Pages: 811 – 840



Heer Zhao (Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, United Kingdom)


For any split totally degenerate abelian variety over a complete discrete valuation field, we construct a log abelian variety, in the sense of [KKN08a], over the discrete valuation ring extending the given abelian variety. This generalizes Kato’s log Tate curve.


degeneration, log abelian varieties

2010 Mathematics Subject Classification

Primary 14K99. Secondary 14D06.

Received 17 October 2016

Accepted 1 November 2016

Published 9 November 2018