nLab
fpqc topology

Contents

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 induced morphism U iX\coprod U_i \to X is faithfully flat and quasicompact. In particular, the union of images then cover XX as a topological space. 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

Last revised on August 19, 2019 at 10:14:08. See the history of this page for a list of all contributions to it.