Algebraic Geometry over model categories (a general approach to derived algebraic geometry)
| dc.creator | Toen, Bertrand | |
| dc.creator | Vezzosi, Gabriele | |
| dc.date | 2001-10-10 | |
| dc.date.accessioned | 2026-07-07T04:43:45Z | |
| dc.date.available | 2026-07-07T04:43:45Z | |
| dc.description | For a (semi-)model category M, we define a notion of a ''homotopy'' Grothendieck topology on M, as well as its associated model category of stacks. We use this to define a notion of geometric stack over a symmetric monoidal base model category; geometric stacks are the fundamental objects to "do algebraic geometry over model categories". We give two examples of applications of this formalism. The first one is the interpretation of DG-schemes as geometric stacks over the model category of complexes and the second one is a definition of etale K-theory of E_{\infty}-ring spectra. This first version is very preliminary and might be considered as a detailed research announcement. Some proofs, more details and more examples will be added in a forthcoming version. | |
| dc.description | LaTeX,xy-pic, 51 pages | |
| dc.identifier | https://arxiv.org/abs/math/0110109 | |
| dc.identifier | http://arxiv.org/abs/math/0110109 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62363 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Algebraic Topology | |
| dc.subject | 14A20; 18G55; 55P43; 55U40;18F10 | |
| dc.title | Algebraic Geometry over model categories (a general approach to derived algebraic geometry) | |
| dc.type | text |