# The derived deformation theory of a point

@article{Booth2020TheDD,
title={The derived deformation theory of a point},
author={Matt Booth},
journal={Mathematische Zeitschrift},
year={2020},
volume={300},
pages={3023-3082}
}
• 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…
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