# Artin's theorems in supergeometry

@inproceedings{Ott2021ArtinsTI, title={Artin's theorems in supergeometry}, author={Nadia Ott}, year={2021} }

We generalize Artin’s three main algebraicity theorems to the setting of supergeometry: approximation [Art69a], algebraization of formal deformations [Art69b], and algebraization of stacks [Art74].

## References

SHOWING 1-10 OF 20 REFERENCES

Artin’s criteria for algebraicity revisited

- MathematicsAlgebra & Number Theory
- 2019

Using notions of homogeneity, as developed in (Hal12b), we give new proofs of M. Artin's algebraicity criteria for functors (Art69b, Thm. 5.3) and groupoids (Art74, Thm. 5.3). Our methods give a more…

The moduli space of stable supercurves and its canonical line bundle

- Mathematics
- 2020

We prove that the moduli of stable supercurves with punctures is a smooth proper DM stack and study an analog of the Mumford's isomorphism for its canonical line bundle.

Deformation of complex superspaces and coherent sheaves on them

- Mathematics
- 1990

This paper sets forth the basic elements of the theory of complex superspaces, coherent sheaves on them and deformations of these objects. The existence of versal deformations is proved for various…

Algebraic Geometry

- Nature
- 1973

Introduction to Algebraic Geometry.By Serge Lang. Pp. xi + 260. (Addison–Wesley: Reading, Massachusetts, 1972.)

Analytic geometry of complex superspaces

- Mathematics
- 1992

A detailed account of the analytic geometry of complex superspaces is given in this paper. Several representability criteria and representability theorems are proved. In particular, the existence of…

OPENNESS OF VERSALITY VIA COHERENT FUNCTORS

- Mathematics
- 2012

We give a proof of openness of versality using coherent functors. As an application, we streamline Artin's criterion for algebraicity of a stack. We also introduce multi-step obstruction theories,…

Approximation of versal deformations

- Mathematics
- 2002

In Artin’s work on algebraic spaces and algebraic stacks [A2], [A3], a crucial ingredient is the use of his approximation theorem to prove the algebraizability of formal deformations under quite…

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…

General NÃ©ron desingularization and approximation

- Mathematics
- 1986

Let A be a noetherian ring (all the rings are supposed here to be commutative with identity), a ⊂ A a proper ideal and Â the completion of A in the α -adic topology. We consider the following…

Versal deformations and algebraic stacks

- Mathematics
- 1974

1. Basic Terminology . . . . . . . . . . . . . . . 166 2. A Review of Schlessinger's Conditions . . . . . . 167 3. Existence of Versal Deformations at a Point . . . . 169 4. Formal Versality in a…