# Homological Algebra for Superalgebras of Differentiable Functions

@article{Carchedi2012HomologicalAF, title={Homological Algebra for Superalgebras of Differentiable Functions}, author={David R. Carchedi and Dmitry Roytenberg}, journal={arXiv: Algebraic Geometry}, year={2012} }

This is the second in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we extend the classical notion of a dg-algebra to define, in particular, the notion of a differential graded algebra in the world of C-infinity rings. The opposite of the category of differential graded C-infinity algebras contains the category of differential graded manifolds as a full subcategory. More…

## 23 Citations

### On Theories of Superalgebras of Differentiable Functions

- Mathematics
- 2012

This is the first in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we…

### Dg Manifolds, Formal Exponential Maps and Homotopy Lie Algebras

- MathematicsCommunications in Mathematical Physics
- 2022

This paper is devoted to the study of the relation between ‘formal exponential maps,’ the Atiyah class, and Kapranov L∞[1] algebras associated with dg manifolds in the C ∞ context. We prove that, for…

### 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…

### Graded Geometry, Q‐Manifolds, and Microformal Geometry

- MathematicsFortschritte der Physik
- 2019

We give an exposition of graded and microformal geometry, and the language of Q‐manifolds. Q‐manifolds are supermanifolds endowed with an odd vector field of square zero. They can be seen as a…

### Derived Differential Geometry

- Mathematics
- 2020

We develop the theory of derived differential geometry in terms of bundles of curved $L_\infty[1]$-algebras, i.e. dg manifolds of positive amplitudes. We prove the category of derived manifolds is a…

### RATIONAL COHOMOLOGY FROM SUPERSYMMETRIC FIELD THEORIES

- Mathematics
- 2014

We show that Sullivan's model of rational differential forms on a simplicial set X may be interpreted as a (kind of) 0|1- dimensional supersymmetric quantum field theory over X, and, as a…

### A differential graded model for derived analytic geometry

- MathematicsAdvances in Mathematics
- 2020

### Shifted symplectic structures on derived analytic moduli of $\ell$-adic local systems and Galois representations

- Mathematics
- 2022

. We develop a characterisation of non-Archimedean derived analytic geometry based on dg enhancements of dagger algebras. This allows us to formulate derived analytic moduli functors for many types…

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This is the first in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we…

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