Descente pour les n-champs (Descent for n-stacks)
| dc.creator | Hirschowitz, André | |
| dc.creator | Simpson, Carlos | |
| dc.date | 1998-07-09 | |
| dc.date | 2001-03-13 | |
| dc.date.accessioned | 2026-07-07T05:25:20Z | |
| dc.date.available | 2026-07-07T05:25:20Z | |
| dc.description | We develop the theory of n-stacks (or more generally Segal n-stacks which are $\infty$-stacks such that the morphisms are invertible above degree n). This is done by systematically using the theory of closed model categories (cmc). Our main results are: a definition of n-stacks in terms of limits, which should be perfectly general for stacks of any type of objects; several other characterizations of n-stacks in terms of ``effectivity of descent data''; construction of the stack associated to an n-prestack; a strictification result saying that any ``weak'' n-stack is equivalent to a (strict) n-stack; and a descent result saying that the (n+1)-prestack of n-stacks (on a site) is an (n+1)-stack. As for other examples, we start from a ``left Quillen presheaf'' of cmc's and introduce the associated Segal 1-prestack. For this situation, we prove a general descent result, giving sufficient conditions for this prestack to be a stack. This applies to the case of complexes, saying how complexes of sheaves of $\Oo$-modules can be glued together via quasi-isomorphisms. This was the problem that originally motivated us. | |
| dc.description | An error in Lemma 6.2 (pointed out by D. Dugger) is partially fixed and 6.1, 6.3, 10.11, 12.1, 14.4, 15.9, 19.4, 21.1 are modified accordingly; the descent 21.1 is now stated only for complexes bounded below | |
| dc.identifier | https://arxiv.org/abs/math/9807049 | |
| dc.identifier | http://arxiv.org/abs/math/9807049 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77142 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Algebraic Topology | |
| dc.subject | Category Theory | |
| dc.title | Descente pour les n-champs (Descent for n-stacks) | |
| dc.type | text |