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 union of images cover $X$ as a topological space and all morphisms $f_i$ 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

category: algebraic geometry

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