locally free

A sheaf of 𝒪X-modules on a ringed space X is called locally free if for each point pX, there is an open neighborhood (http://planetmath.org/NeighborhoodMathworldPlanetmath) U of x such that |U is free (http://planetmath.org/FreeModule) as an 𝒪X|U-module, or equivalently, p, the stalk of at p, is free as a (𝒪X)p-module. If p is of finite rank (http://planetmath.org/ModuleOfFiniteRank) n, then is said to be of rank n.

Title locally free
Canonical name LocallyFree
Date of creation 2013-03-22 13:52:31
Last modified on 2013-03-22 13:52:31
Owner mps (409)
Last modified by mps (409)
Numerical id 13
Author mps (409)
Entry type Definition
Classification msc 14A99