nLab Serre's criterion of affineness

Redirected from "higher chromatic Chern characters".
Note: higher chromatic Chern character, higher chromatic Chern character, and higher chromatic Chern character all redirect for "higher chromatic Chern characters".

Serre’s criterion of affineness characterizes affine morphisms of schemes in terms of exactness properties of the corresponding functors among the categories of quasicoherent sheaves.

If $f\colon X\to Y$ is a quasicompact morphism of algebraic schemes and $X$ is separated, then $f$ is affine iff it is cohomologically affine, that is, the direct image functor $f_*$ is exact.

EGA II 5.2.2, EGA IV 1.7.17
Akhil Mathew, Serre’s criterion for affineness as Morita theory, a blog post

Last revised on February 5, 2014 at 07:53:02. See the history of this page for a list of all contributions to it.