The local obstruction to semi-stable reduction for abelian varieties
Séverin Philip1
1Department of Mathematics, Stockholms Universitet, SE-106 91 Stockholm, Sweden
Mathematics Research Reports, Volume 7 (2026), pp. 45-58

Grothendieck defined a group that represents the local obstruction for an abelian variety to have semi-stable reduction. These groups were studied by Silverberg and Zarhin and more recently by the author in order to give a group theoretic characterization of them depending only on the dimension. We give an overview of the developments since Grothendieck’s definition with the added novelty of the case of equal characteristic local fields.

Received:
Revised:
Published online:
DOI: 10.5802/mrr.26
Classification: 11G25, 14K15, 20C05
Keywords: abelian varieties, semi-stable reduction, finite monodromy groups

Séverin Philip  1

1 Department of Mathematics, Stockholms Universitet, SE-106 91 Stockholm, Sweden
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Séverin Philip. The local obstruction to semi-stable reduction for abelian varieties. Mathematics Research Reports, Volume 7 (2026), pp. 45-58. doi: 10.5802/mrr.26
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