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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References

SHOWING 1-10 OF 112 REFERENCES

Noncommutative deformations and flops

We prove that the functor of noncommutative deformations of every flipping or flopping irreducible rational curve in a 33-fold is representable, and hence, we associate to every such curve a

Noncommutative deformations of modules

The classical deformation theory for modules on a k-algebra, where k is a Þeld, is generalized. For any k-algebra, and for any Þnite family of r modules, we consider a deformation functor deÞned on

An introduction to noncommutative deformations of modules

This paper gives an elementary introduction to noncommutative deformations of modules. The main results of this deformation theory are due to Laudal. Let k be an algebraically closed (commutative)

Unifying derived deformation theories

The homotopy theory of dg-categories and derived Morita theory

The main purpose of this work is to study the homotopy theory of dg-categories up to quasi-equivalences. Our main result is a description of the mapping spaces between two dg-categories C and D in

DG coalgebras as formal stacks

...