The derived deformation theory of a point

  title={The derived deformation theory of a point},
  author={Matt Booth},
  journal={Mathematische Zeitschrift},
  • Matt Booth
  • Published 3 September 2020
  • Mathematics
  • Mathematische Zeitschrift
We provide a prorepresenting object for the noncommutative derived deformation problem of deforming a module $X$ over a differential graded algebra. Roughly, we show that the corresponding deformation functor is homotopy prorepresented by the dual bar construction on the derived endomorphism algebra of $X$. We specialise to the case when $X$ is one-dimensional over the base field, and introduce the notion of framed deformations, which rigidify the problem slightly and allow us to obtain derived… Expand
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