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SUMMARY:Models of curves via Berkovich geometry
DTSTART:20221013T101500
DTEND:20221013T120000
DTSTAMP:20260506T165058Z
UID:6b15cace8078284ac880f523d7acdd3be619f32038091a4abe0bc8b9
CATEGORIES:Conferences - Seminars
DESCRIPTION:Daniele Turchetti (University of Warwick)\nThe theory of model
 s of varieties is an important tool for topics such as deformation theory\
 , moduli spaces\, and degenerations. In the 1960s\, Deligne and Mumford pr
 oved that any smooth projective curve C over a discretely valued field K h
 as a semi-stable model after base-change to a finite Galois extension L|K.
  The question of determining such extension has been investigated ever sin
 ce but has been settled only in the case where L|K is tamely ramified.\nIn
  this talk\, I will present two results on the behaviour of models of curv
 es under finite base-change. The first (joint with Lorenzo Fantini) exploi
 ts the geometry of the Berkovich analytification of C to describe the exte
 nsion L|K in terms of regular models\; the second (joint with Andrew Obus)
  investigates more in detail the case of potentially multiplicative reduct
 ion yielding new results in the case where L|K is wildly ramified.
LOCATION:GR A3 32 https://plan.epfl.ch/?room==GR%20A3%2031
STATUS:CONFIRMED
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