arXiv:0909.4425 Reduction of Abelian Varieties and Grothendieck’s Pairing from arXiv Front: math.AG by Klaus Loerke We prove that abelian varieties of small dimension over discrete valuated, stricty henselian ground fields with perfect residue class field obtain semistable reduction after a tamely ramified extension of the ground field. Using this result we obtain perfectness results for Grothendieck’s pairing.
http://mathoverflow.net/questions/77444/semistable-reduction-theorem-over-higher-dimensional-schemes
http://mathoverflow.net/questions/110810/dual-reduction-graph-of-a-curve
[arXiv:1207.1048] A tour of stable reduction with applications fra arXiv Front: math.AG av Sebastian Casalaina-Martin The Deligne-Mumford stable reduction theorem asserts that for a family of stable curves over the punctured disk, after a finite base change, the family can be completed in a unique way to a family of stable curves over the disk. In this survey, we discuss stable reduction theorems in a number of different contexts. This includes a review of recent results on abelian varieties, canonically polarized varieties, and singularities. We also consider the Semi-Stable Reduction Theorem and results concerning simultaneous stable reduction.
nLab page on Semistable reduction