# Koszul duality for Lie algebroids

@article{Nuiten2019KoszulDF,
title={Koszul duality for Lie algebroids},
author={Joost Nuiten},
year={2019}
}
• J. Nuiten
• Published 9 December 2017
• Mathematics
11 Citations

### Homotopical Algebra for Lie Algebroids

• J. Nuiten
• Mathematics
Appl. Categorical Struct.
• 2019
It is shown how Lie algebroid cohomology is represented by an object in the homotopy category of dg-Lie algebroids.

### Lie algebroids are curved Lie algebras

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We show that there is an equivalence of ∞-categories between Lie algebroids and certain kinds of curved Lie algebras. For this we develop a method to study the ∞category of curved Lie algebras using

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Journal of the London Mathematical Society
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A classical principle in deformation theory asserts that any formal deformation problem is controlled by a differential graded Lie algebra. This thesis studies a generalization of this principle to

### Poisson Geometry of the Moduli of Local Systems on Smooth Varieties

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Publications of the Research Institute for Mathematical Sciences
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We study the moduli of G-local systems on smooth but not necessarily proper complex algebraic varieties. We show that, when suitably considered as derived algebraic stacks, they carry natural Poisson

### Shifted Symplectic Lie Algebroids

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International Mathematics Research Notices
• 2018
Shifted symplectic Lie and $L_{\infty }$ algebroids model formal neighborhoods of manifolds in shifted symplectic stacks and serve as target spaces for twisted variants of the classical topological

### The integration theory of curved absolute L-infinity algebras

A BSTRACT . In this article, we introduce the notion of a curved absolute L ∞ -algebra, a structure that behaves like a curved L ∞ -algebra where all inﬁnite sums of operations are well-deﬁned by

### Formal moduli problems and formal derived stacks

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• 2018
This paper presents a survey on formal moduli problems. It starts with an introduction to pointed formal moduli problems and a sketch of proof of a Theorem (independently proven by Lurie and Pridham)

### Moduli of ﬂat connections on smooth varieties

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• 2019
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### Non-archimedean quantum K-invariants

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• 2020
We construct quantum K-invariants in non-archimedean analytic geometry. Our approach differs from the classical one in algebraic geometry via perfect obstruction theory. Instead, we build on our

## References

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### Homotopical Algebra for Lie Algebroids

• J. Nuiten
• Mathematics
Appl. Categorical Struct.
• 2019
It is shown how Lie algebroid cohomology is represented by an object in the homotopy category of dg-Lie algebroids.

### A model structure on relative dg-Lie algebroids

In this Note, for the future purposes of relative formal derived deformation theory and of derived coisotropic structures, we prove the existence of a model structure on the category of dg-Lie

### Deformations of Homotopy Algebras

Abstract Let k be a field of characteristic zero, 𝒪 be a dg operad over k and let A be an 𝒪-algebra. In this note we suggest a definition of a formal deformation functor of A from the category of

### The homotopy category of flat modules, and Grothendieck duality

Let R be a ring. We prove that the homotopy category K(R-Proj) is always $\aleph_1$-compactly generated, and, depending on the ring R, it may or may not be compactly generated. We use this to give a

### Lie Groupoids and Lie Algebroids in Differential Geometry

Introduction 1. The algebra of groupoids 2. Topological groupoids 3. Lie groupoids and Lie algebroids 4. The cohomology of Lie algebroids 5. An obstruction to the integrability of transitive Lie

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• Benjamin Hennion
• Mathematics
Journal für die reine und angewandte Mathematik (Crelles Journal)
• 2018
Since the work of Mikhail Kapranov in [Compos. Math. 115 (1999), no. 1, 71–113], it is known that the shifted tangent complex \mathbb{T}_{X} [-1] of a smooth algebraic variety X is

### Functors of Artin rings

0. Introduction. In the investigation of functors on the category of preschemes, one is led, by Grothendieck [3], to consider the following situation. Let A be a complete noetherian local ring, ,u

### Deformation Quantization of Poisson Manifolds

I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the