Raptis, Georgios and Strunk, Florian (2018) MODEL TOPOI AND MOTIVIC HOMOTOPY THEORY. DOCUMENTA MATHEMATICA, 23. pp. 1757-1797. ISSN 1431-0643,
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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 presheaves on C where the weak equivalences are the local weak equivalences of the underlying (non-enriched) simplicial presheaves. We show that this model category is a t-complete model topos and describe the Grothendieck topology [tau] on the homotopy category of C that corresponds to this model topos. After we first review a proof showing that the motivic homotopy theory is not a model topos, we specialize this construction to the category of smooth schemes of finite type, which is simplicially enriched using the standard algebraic cosimplicial object, and compare the result with the motivic homotopy theory. We also collect some partial positive results on the exactness properties of the motivic, localization functor.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SIMPLICIAL PRESHEAVES; A(1)-HOMOTOPY THEORY; PULL-BACKS; Motivic homotopy theory; Topoi |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 20 Mar 2020 05:35 |
| Last Modified: | 20 Mar 2020 05:35 |
| URI: | https://pred.uni-regensburg.de/id/eprint/15226 |
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