# 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} }

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…

## 3 Citations

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. We provide an outline of the proof of the Donovan–Wemyss Con- jecture in the context of the Homological Minimal Model Program for threefolds. The proof relies on results of August, of Hua and the…

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