Wild ramification kinks
Andrew Obus, Stefan Wewers

TL;DR
This paper investigates conditions under which the inverse image of an open disk under a branched cover of smooth projective curves remains an open disk, especially within families of covers over non-archimedean fields.
Contribution
It provides a criterion determining when the inverse image of an open disk under a branched cover is again an open disk, including in analytic families of covers.
Findings
Criteria for inverse image of open disks to be open disks
Results on stability of disk preimages in families of covers
Insights into ramification behavior in non-archimedean geometry
Abstract
Given a branched cover between smooth projective curves over a non-archimedian mixed-characteristic local field and an open rigid disk , we study the question under which conditions the inverse image is again an open disk. More generally, if the cover varies in an analytic family, is this true at least for some member of the family? Our main result gives a criterion for this to happen.
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Taxonomy
TopicsPolysaccharides Composition and Applications · Coastal wetland ecosystem dynamics · Aeolian processes and effects
