## 11 Citations

### Homotopical Algebra for Lie Algebroids

- MathematicsAppl. 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

- Mathematics
- 2021

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…

### Moduli problems for operadic algebras

- MathematicsJournal of the London Mathematical Society
- 2022

A theorem of Pridham and Lurie provides an equivalence between formal moduli problems and Lie algebras in characteristic zero. We prove a generalization of this correspondence, relating formal moduli…

### Lie algebroids in derived differential topology

- Mathematics
- 2018

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

- MathematicsPublications of the Research Institute for Mathematical Sciences
- 2021

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

- MathematicsInternational 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

- Mathematics
- 2022

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

- Mathematics
- 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

- Mathematics
- 2019

We study the moduli functor of flat bundles on smooth, possibly non-proper, algebraic variety $X$ (over a field of characteristic zero). For this we introduce the notion of \emph{formal boundary} of…

### Non-archimedean quantum K-invariants

- Mathematics
- 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

SHOWING 1-10 OF 40 REFERENCES

### Homotopical Algebra for Lie Algebroids

- MathematicsAppl. 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

- Mathematics
- 2013

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

- Mathematics
- 1999

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

- Mathematics
- 2008

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

- Mathematics
- 1987

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…

### Tangent Lie algebra of derived Artin stacks

- MathematicsJournal 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

- Mathematics
- 1968

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

- Mathematics
- 1997

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…