Descent for Coherent Sheaves on Rigid-analytic Spaces

If one assumes k to have a discrete valuation, then descent theory for coherent sheaves is an old result of Gabber. Gabber’s method was extended to the general case by Bosch and Görtz [BG]. Our method is rather different from theirs (though both approaches do use Raynaud’s theory of formal models [BL1], [BL2], we use less of this theory). We think that our approach may be of independent interest, because in contrast with all other known examples of descent (at least to this author) the method of proof is to show non-vanishing of the “descent module” before one proves effectivity of descent, and to invoke noetherian induction to obtain the effectivity. Further geometric examples of fpqc descent in the rigid-analytic context are discussed in [C].