Chiral de Rham complex over locally complete intersections

Fyodor Malikov^a, Vadim Schechtman<sup>b

a</sup> Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA
^b Institut de Mathématiques de Toulouse, Université Paul Sabatier, 31062 Toulouse, France

Abstract: Given a locally complete intersection $X\hookrightarrow Y$ we define a version of a derived chiral De Rham complex, thereby “chiralizing” a result by Illusie and Bhatt. A similar construction attaches to a graded ring a dg vertex algebra, which we prove to be Morita equivalent to a dg algebra of differential operators. For example, the dg vertex algebra associated to a fat point, which also arises in the Landau–Ginzburg model, is shown to be derived rational.

Key words and phrases: vertex algebra, chiral differential operator, dga resolution.

MSC: 14, 18

Received: May 30, 2014

Language: English

DOI: 10.17323/1609-4514-2015-15-2-353-372

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