# Contents

## Definition

A morphism $f:Y\to X$ is finitely presented at $x\in X$ if there is an affine open neighborhood $U\ni x$ and an affine open set $V\subset Y$, $f\left(V\right)\subset U$ such that ${𝒪}_{Y}\left(V\right)$ is finitely generated as ${𝒪}_{X}\left(U\right)$-module. A morphism $f:Y\to X$ is locally finitely presented if it is finitely presented at each $x\in X$. It is finitely presented if it is locally finitely presented, quasicompact and quasiseparated.

Morphism is essentially finitely presented if it is a localization of a finitely presented morphism.

Revised on February 13, 2012 02:52:32 by Zoran Škoda (109.227.55.211)