nLab
fpqc topology

Contents

Idea

The fpqc topology is a Grothendieck topology on the category of (commutative) affine schemes. It is one of the main Grothendieck topologies used in algebraic geometry.

Definition

Let AffAff be the category opposite to the category of commutative algebras. A family of maps {f i:U iX} iI\{f_i : U_i\to X\}_{i\in I} in that category is a cover in the fpqc topology if the union of images cover XX as a topological space and all morphisms f if_i are faithfully flat and quasicompact. The French for this is fidèlement plat et quasicompact (fpqc).

fpqc-site \to fppf-site \to syntomic site \to étale site \to Nisnevich site \to Zariski site

Revised on November 20, 2013 06:20:34 by Urs Schreiber (82.169.114.243)