## 281 Citations

### Homotopical Algebraic Geometry II: Geometric Stacks and Applications

- Mathematics
- 2004

This is the second part of a series of papers devoted to develop Homotopical Algebraic Geometry. We start by defining and studying generalizations of standard notions of linear and commutative…

### MODULI OF OBJECTS IN DG-CATEGORIES BY BERTRAND TOËN

- 2007

– The purpose of this work is to prove the existence of an algebraic moduli classifying objects in a given triangulated category. To any dg-category T (over some base ring k), we define a D−-stack MT…

### A pr 2 00 3 MODEL STRUCTURES AND THE OKA PRINCIPLE

- Mathematics

We embed the category of complex manifolds into the simplicial category of prestacks on the simplicial site of Stein manifolds, a prestack being a contravariant simplicial functor from the site to…

### On the homotopy theory of $n$-types

- Mathematics
- 2006

An n-truncated model structure on simplicial (pre-)sheaves is described having as weak equivalences maps that induce isomorphisms on certain homotopy sheaves only up to degree n. Starting from one of…

### A Projective Model Structure on Pro Simplicial Sheaves, and the Relative \'Etale Homotopy Type

- Mathematics
- 2011

### Segal topoi and stacks over Segal categories

- Mathematics
- 2002

In math.AG/0207028 we began the study of higher sheaf theory (i.e. stacks theory) on higher categories endowed with a suitable notion of topology: precisely, we defined the notions of S-site and of…

### Model topoi and motivic homotopy theory

- Mathematics
- 2017

Given a small simplicial category $\C$ whose underlying ordinary category is equipped with a Grothendieck topology $\tau$, we construct a model structure on the category of simplicially enriched…

### Derived Algebraic Geometry Over & E-Rings by

- Mathematics
- 2008

We develop a theory of less commutative algebraic geometry where the role of commutative rings is assumed by En-rings, that is, rings with multiplication parametrized by configuration spaces of…

### Under Spec Z

- Mathematics
- 2005

We use techniques from relative algebraic geometry and homotopical algebraic geometry in order to construct several categories of schemes defined "under Spec Z". We define this way the categories of…

### Categorical Foundations for K-theory

- Mathematics
- 2010

K-Theory was originally defined by Grothendieck as a contravariant functor from a subcategory of schemes to abelian groups, known today as K0. The same kind of construction was then applied to other…

## References

SHOWING 1-10 OF 112 REFERENCES

### Homotopical Algebraic Geometry II: Geometric Stacks and Applications

- Mathematics
- 2004

This is the second part of a series of papers devoted to develop Homotopical Algebraic Geometry. We start by defining and studying generalizations of standard notions of linear and commutative…

### Local Projective Model Structures on Simplicial Presheaves

- Mathematics
- 2001

We give a model structure on the category of simplicial presheaves on some essentially small Grothendieck site T . When T is the Nisnevich site it specializes to a proper simplicial model category…

### Simplicial functors and stable homotopy theory

- Mathematics
- 1998

The problem of constructing a nice smash product of spectra is an old and well-known problem of algebraic topology. This problem has come to mean the following: Find a model category, which is…

### From Hag To Dag: Derived Moduli Stacks

- Mathematics
- 2004

These are expanded notes of some talks given during the fall 2002, about homotopical algebraic geometry with special emphasis on its applications to derived algebraic geometry and derived deformation…

### Axiomatic, enriched, and motivic homotopy theory

- Mathematics
- 2004

Contributing Authors. Preface. Part I: General surveys. Localizations W.G. Dwyer. 1. Introduction. 2. Algebra. 3. Homological localization in topology. 4. Localization with respect to a map. 5.…

### Brave new algebraic geometry and global derived moduli spaces of ring spectra

- Mathematics
- 2003

We develop homotopical algebraic geometry ([To-Ve 1, To-Ve 2]) in the special context where the base symmetric monoidal model category is that of spectra S, i.e. what might be called, after…

### Homotopy Algebras for Operads

- Mathematics
- 2000

We present a definition of homotopy algebra for an operad, and explore its consequences.
The paper should be accessible to topologists, category theorists, and anyone acquainted with operads. After…