arXiv:1206.3439 Pure morphisms are effective for modules from arXiv Front: math.CT by Bachuki Mesablishvili Yet another proof of the result asserting that a morphism of commutative rings is an effective descent morphism for modules if and only if it is pure is given. Moreover, it is shown that this result cannot be derived from Moerdijk’s descent criterion.
http://mathoverflow.net/questions/34904/when-does-a-vector-bundle-descent
On proper descent for crystalline cohomology (fails): http://math.columbia.edu/~dejong/wordpress/?p=2201
arXiv:1211.1813 Pro excision and h-descent for K-theory fra arXiv Front: math.AG av Matthew Morrow In this paper it is proved that K-theory (and Hochschild and cyclic homology) satisfies pro versions of both excision for ideals (of commutative Noetherian rings) and descent in the h-topology in characteristic zero; this is achieved by passing to the limit over all infinitesimal thickenings of the ideal or exceptional fibre in question.
nLab page on Descent III