  The goal of this paper is to prove a Koszul duality result for E_n-operads in
differential graded modules over a ring. The case of an E_1-operad, which is
equivalent to the associative operad, is classical. For n>1, the homology of an
E_n-operad is identified with the n-Gerstenhaber operad and forms another well
known Koszul operad. Our main theorem asserts that an operadic cobar
construction on the dual cooperad of an E_n-operad defines a cofibrant model of
E_n. This cofibrant model gives a realization at the chain level of the minimal
model of the n-Gerstenhaber operad arising from Koszul duality.
  Most models of E_n-operads in differential graded modules come in nested
sequences of operads homotopically equivalent to the sequence of the chain
operads of little cubes. In our main theorem, we also define a model of the
operad embeddings E_n-1 --> E_n at the level of cobar constructions.
