Displaying similar documents to “Vanishing of Hochschild cohomology for affine group schemes and rigidity of homomorphisms between algebraic groups.”

Vertex algebras and the formal loop space

Mikhail Kapranov, Eric Vasserot (2004)

Publications Mathématiques de l'IHÉS

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We construct a certain algebro-geometric version ( X ) of the free loop space for a complex algebraic variety X. This is an ind-scheme containing the scheme 0 ( X ) of formal arcs in X as studied by Kontsevich and Denef-Loeser. We describe the chiral de Rham complex of Malikov, Schechtman and Vaintrob in terms of the space of formal distributions on ( X ) supported in 0 ( X ) . We also show that ( X ) possesses a factorization structure: a certain non-linear version of a vertex algebra structure. This explains...