Homotopical algebraic geometry. I. Topos theory.

@article{Toen2002HomotopicalAG,
  title={Homotopical algebraic geometry. I. Topos theory.},
  author={Bertrand Toen and Gabriele Vezzosi},
  journal={Advances in Mathematics},
  year={2002},
  volume={193},
  pages={257-372}
}
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281 Citations
Highly Influential Citations
19
Background Citations
45
Methods Citations
30
Results Citations
1

281 Citations

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Homotopical Algebraic Geometry II: Geometric Stacks and Applications

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…

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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…

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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…

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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.…

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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…

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