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Moduli spaces of algebras over non-symmetric operads

 

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Author: Muro Jiménez, Fernando
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2014
Published in: Algebraic & Geometric Topology, 14 (3), 1489-1539.
Document type: Article
Abstract: In this paper we study spaces of algebras over an operad (nonsymmetric) in symmetric monoidal model categories. We first compute the homotopy fiber of the forgetful functor sending an algebra to its underlying object, extending a result of Rezk. We then apply this computation to the construction of geometric moduli stacks of algebras over an operad in a homotopical algebraic geometry context in the sense of To¨en and Vezzosi. We show under mild hypotheses that the moduli stack of unital associative algebras is a Zariski open substack of the moduli stack of non-necessarily unital associative algebras. The classical analogue for finite-dimensional vector spaces was noticed by Gabriel.
Cite: Muro Jiménez, F. (2014). Moduli spaces of algebras over non-symmetric operads. Algebraic & Geometric Topology, 14 (3), 1489-1539.
Size: 457.1Kb
Format: PDF

URI: http://hdl.handle.net/11441/41878

DOI: http://dx.doi.org/10.2140/agt.2014.14.1489

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