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SUMMARY:A criterion for existence of Néron models
DTSTART:20191010T151500
DTEND:20191010T164500
DTSTAMP:20260916T063147Z
UID:0e8b608b92829dbc22ff8c31bb5cf5481bff6c1a276fe38901c1aab4
CATEGORIES:Conferences - Seminars
DESCRIPTION:Giulio Orecchia (Université de Rennes 1)\nGiven an abelian va
 riety A over the fraction field K of a Dedekind domain R\, there is a cano
 nical model for A over R\, called Néron model. It enjoys a number of usef
 ul properties. However\, if K is the fraction field of a higher dimensiona
 l ring R\, there may be no Néron model for A. In the first 30 minutes\, I
  will introduce Néron models\, motivate their definition\, and show an ex
 ample of jacobian not admitting a Néron model over a 2-dimension base. In
  the following 45 minutes\, I will introduce a criterion\, called toric ad
 ditivity\, for an abelian family with semistable reduction to admit a Nér
 on model over a higher dimensional base scheme. If time allows\, I will di
 scuss work in progress about how logarithmic jacobians constitute a good r
 eplacement for Néron models.
LOCATION:GR C0 01 https://plan.epfl.ch/?room==GR%20C0%2001
STATUS:CONFIRMED
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