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SUMMARY:Singular Supports in Equal and Mixed Characteristics
DTSTART:20250929T083000Z
DTEND:20250929T103000Z
DTSTAMP:20260423T021500Z
UID:indico-event-14412@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Takeshi Saito (The University of Tokyo & IHES)\n\nBe
 ilinson defined the singular support of a constructible sheaf on a smooth 
 scheme over a field as a closed conical subset on the cotangent bundle. He
  further proved its existence and fundamental properties\, using Radon tra
 nsform as a crucial tool. In first lectures\, we formulate the definition 
 in a slightly different but equivalent way\, using an interpretation by Br
 averman--Gaitsgory of the local acycliciity. We also recall Beilinson's pr
 oof of existence.\nIn mixed characteristics\, the theory is still far from
  complete. As a replacement of the cotangent bundle\, we introduce the Fro
 benius--Witt cotangent bundle\, that has the correct rank but defined only
  on the characteristic p fiber. Using it\, we define  the singular suppor
 t and its relative variant. Finally\, we show that Beilinson's argument us
 ing the Radon transform gives a proof of the existence of the saturation o
 f the relative variant.\n\nhttps://indico.math.cnrs.fr/event/14412/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/14412/
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