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SUMMARY:Koszul Duality for Lie Algebroids
DTSTART;VALUE=DATE-TIME:20200302T143000Z
DTEND;VALUE=DATE-TIME:20200302T153000Z
DTSTAMP;VALUE=DATE-TIME:20221001T114400Z
UID:indico-event-5714@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Joost-Jakob Nuiten (Montpellier)\n\nA classical prin
ciple in deformation theory asserts that any formal deformation problem ov
er a field of characteristic zero is classified by a differential graded L
ie algebra. Using the Koszul duality between Lie algebras and commutative
algebras\, Lurie and Pridham have given a more precise description of this
principle: they establish an equivalence of categories between dg-Lie alg
ebras and formal moduli problems indexed by Artin commutative dg-algebras.
I will describe a variant of this result for deformation problems around
schemes over a field of characteristic zero. In this case\, there is an eq
uivalence between the homotopy categories of dg-Lie algebroids and formal
moduli problems on a derived scheme. This can be viewed as a derived versi
on of the relation between Lie algebroids and formal groupoids.\n\nhttps:/
/indico.math.cnrs.fr/event/5714/
LOCATION:Centre de confĂ©rences Marilyn et James Simons (IHES)
URL:https://indico.math.cnrs.fr/event/5714/
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