000143870 001__ 143870
000143870 005__ 20181203021808.0
000143870 037__ $$aARTICLE 000143870 245__$$aA general framework for homotopic descent and codescent
000143870 336__ $$aJournal Articles 000143870 520__$$aIn this paper we elaborate a general homotopy-theoretic framework in which to study problems of descent and completion and of their duals, codescent and cocompletion. Our approach to homotopic (co)descent and to derived (co)completion can be viewed as $\infty$-category-theoretic, as our framework is constructed in the universe of simplicially enriched categories, which are a model for $(\infty, 1)$-categories. We provide general criteria, reminiscent of Mandell's theorem on $E_{\infty}$-algebra models of $p$-complete spaces, under which homotopic (co)descent is satisfied. Furthermore, we construct general descent and codescent spectral sequences, which we interpret in terms of derived (co)completion and homotopic (co)descent. We prove that Baum-Connes and Farrell-Jones-type isomorphism conjectures for assembly can be expressed in the language of derived cocompletion and show that a number of very well-known spectral sequences, such as the unstable and stable Adams spectral sequences, the Adams-Novikov spectral sequence and the descent spectral sequence of a map, are examples of general (co)descent spectral sequences. There is also a close relationship between the Lichtenbaum-Quillen conjecture and homotopic descent along the Dwyer-Friedlander map from algebraic K-theory to etale K-theory.
000143870 700__ $$0240499$$aHess, Kathryn$$g105396 000143870 773__$$tpreprint
000143870 8564_ $$uhttp://arxiv.org/abs/1001.1556$$zURL
000143870 8564_ $$s621915$$uhttps://infoscience.epfl.ch/record/143870/files/1001.1556v1.pdf$$zn/a 000143870 909C0$$0252139$$pUPHESS$$xU10968
000143870 909CO $$ooai:infoscience.tind.io:143870$$pSV$$pGLOBAL_SET$$particle
000143870 937__ $$aGR-HE-ARTICLE-2010-001 000143870 973__$$aEPFL$$rREVIEWED$$sSUBMITTED
000143870 980__ aARTICLE