The derived deformation theory of a point
نویسندگان
چکیده
We provide a prorepresenting object for the noncommutative derived deformation problem of deforming module $X$ over differential graded algebra. Roughly, we show that corresponding functor is homotopy prorepresented by dual bar construction on endomorphism algebra $X$. specialise to case when one-dimensional base field, and introduce notion framed deformations, which rigidify slightly allow us obtain analogues results Ed Segal's thesis. Our main technical tool Koszul duality, following Pridham Lurie's interpretation theory. Along way prove large class dgas are quasi-isomorphic their double dual, interpret as completion functor; this improves theorem Lu-Palmieri-Wu-Zhang. also adapt our setting multi-pointed theory, furthermore give an analysis universal prodeformations. As application, deformation-theoretic Braun-Chuang-Lazarev's quotient.
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2021
ISSN: ['1432-1823', '0025-5874']
DOI: https://doi.org/10.1007/s00209-021-02892-7