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Mosc. Math. J., 2015, Volume 15, Number 2, Pages 353–372 (Mi mmj563)  

Chiral de Rham complex over locally complete intersections

Fyodor Malikova, Vadim Schechtmanb

a 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.

DOI: https://doi.org/10.17323/1609-4514-2015-15-2-353-372

Full text: http://www.mathjournals.org/.../2015-015-002-010.html
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Bibliographic databases:

MSC: 14, 18
Received: May 30, 2014
Language:

Citation: Fyodor Malikov, Vadim Schechtman, “Chiral de Rham complex over locally complete intersections”, Mosc. Math. J., 15:2 (2015), 353–372

Citation in format AMSBIB
\Bibitem{MalSch15}
\by Fyodor~Malikov, Vadim~Schechtman
\paper Chiral de Rham complex over locally complete intersections
\jour Mosc. Math.~J.
\yr 2015
\vol 15
\issue 2
\pages 353--372
\mathnet{http://mi.mathnet.ru/mmj563}
\crossref{https://doi.org/10.17323/1609-4514-2015-15-2-353-372}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3427428}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000361607300010}


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