Given a commutative unital ring there is an equivalence of categories
between the category of -modules and the category of quasicoherent sheaves of -modules given on objects by where is the unique sheaf such that the restriction on the principal Zariski open subsets is given by the localization where is the principal Zariski open set underlying , and the restrictions are given by the canonical maps among the localizations. The action of is defined using a similar description of . Its right adjoint (quasi)inverse functor is given by the global sections functor .
Created on June 1, 2012 at 15:31:37. See the history of this page for a list of all contributions to it.