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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Vydáno v:Advances in mathematics (New York. 1965) Ročník 433; s. 109300
Hlavní autor: Pridham, J.P.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 15.11.2023
Témata:
Derived algebraic geometry
Moduli theory
Noncommutative algebraic geometry
Derived algebraic geometry
Moduli theory
Noncommutative algebraic geometry
primary
ISSN:0001-8708, 1090-2082
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Shrnutí: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