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Deformation Theory Seminar

Wednesday, June 21, 2017 - 2:00pm

Giovanni Faonte

Max Planck Inst - Bonn and Yale


University of Pennsylvania


Originally scheduled May 3, 2017

We provide a generalization
to the higher dimensional case of the construction of the
current algebra g((z)), of its Kac-Moody extension and of the
classical results relating them to the theory of G-bundles
over a curve. For a reductive algebraic group G with Lie
algebra g, we define a dg-Lie algebra g_n of n-dimensional
currents in g. We show that any symmetric G-invariant
polynomial P on g of degree n+1 determines a central extension
of g_n by the base field k that we call higher Kac-Moody
algebra g_{n,P} associated to P. Further, for a smooth,
projective variety X of dimension n>1, we show that g_n
acts infinitesimally on the derived moduli space RBun_G(X,x)
of G-bundles over X trivialized at the formal neighborhood of
a point x of X. If times allow, I will discuss the relation
between  the Kac-Moody extension and the determinantal line
bundle on RBun_G(X,x).