Non-commutative derived moduli prestacks

We introduce a formalism for derived moduli functors on differential graded associative algebras, which leads to non-commutative enhancements of derived moduli stacks and naturally gives rise to structures such as Hall algebras. Descent arguments are not available in the non-commutative context, so...

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Bibliographic Details
Published in:	Advances in mathematics (New York. 1965) Vol. 433; p. 109300
Main Author:	Pridham, J.P.
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 15.11.2023
Subjects:	Derived algebraic geometry Moduli theory Noncommutative algebraic geometry Derived algebraic geometry Moduli theory Noncommutative algebraic geometry primary
ISSN:	0001-8708, 1090-2082
Online Access:	Get full text
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Summary:	We introduce a formalism for derived moduli functors on differential graded associative algebras, which leads to non-commutative enhancements of derived moduli stacks and naturally gives rise to structures such as Hall algebras. Descent arguments are not available in the non-commutative context, so we establish new methods for constructing various kinds of atlases. The formalism permits the development of the theory of shifted bi-symplectic and shifted double Poisson structures in the companion paper [27].
ISSN:	0001-8708 1090-2082
DOI:	10.1016/j.aim.2023.109300