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SUMMARY:The geometric Satake equivalence in mixed characteristic
DTSTART;VALUE=DATE-TIME:20170411T083000Z
DTEND;VALUE=DATE-TIME:20170411T093000Z
DTSTAMP;VALUE=DATE-TIME:20210723T230131Z
UID:indico-event-2228@indico.math.cnrs.fr
DESCRIPTION:In order to apply V. Lafforgue's ideas to the study of represe
ntations of p-adic groups\, one needs a version of the geometric Satake eq
uivalence in that setting. For the affine Grassmannian defined using the W
itt vectors\, this has been proven by Zhu. However\, one actually needs a
version for the affine Grassmannian defined using Fontaine's ring B_dR\, a
nd related results on the Beilinson-Drinfeld Grassmannian over a self-prod
uct of Spa(ℚ_p). These objects exist as diamonds\, and in particular one
can make sense of the fusion product in this situation\; this is a priori
surprising\, as it entails colliding two distinct points of Spec(ℤ). Th
e focus of the talk will be on the geometry of the fusion product\, and an
analogue of the technically crucial ULA (Universally Locally Acyclic) con
dition that works in this non-algebraic setting.\n\nhttps://indico.math.cn
rs.fr/event/2228/
LOCATION:IHES Centre de conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/2228/
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