fpqc topology

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.

Let $Aff$ be the category opposite to the category of commutative algebras. A family of maps $\{f_i : U_i\to X\}_{i\in I}$ in that category is a cover in the **fpqc topology** if the induced morphism $\coprod U_i \to X$ is faithfully flat and quasicompact. In particular, the union of images then cover $X$ 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

category: algebraic geometry

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