A Simple Construction of Derived Representation Schemes
Abstract
We present a simple algebraic construction of the (non-abelian) derived functors DRepn(A) of the representation scheme Repn(A), parametrizing the n-dimensional representations of an associative algebra A. We construct a related derived version of the representation functor introduced recently by M. Van den Bergh and, as an application, compute the derived tangent spaces TDRepn(A) to Repn(A). We prove that our construction of DRepn(A) agrees with an earlier construction of derived action spaces, due to I. Ciocan-Fontanine and M. Kapranov; however, our approach, proofs and motivation are quite different. This paper is mainly a research announcement; detailed proofs and applications will appear elsewhere.
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