Sheaves of Modules
Let be a ringed space. A sheaf of modules is a sheaf such that on every open set U of X, is an -module and for every inclusion of open sets V ⊆ U, the restriction map is a homomorphism of -modules.
Most important geometric objects are sheaves of modules. For example, there is a one-to-one correspondence between vector bundles and locally free sheaves of -modules. Sheaves of solutions to differential equations are D-modules, that is, modules over the sheaf of differential operators.
A particularly important case are abelian sheaves, which are modules over the constant sheaf . Every sheaf of modules is an abelian sheaf.
Read more about this topic: Sheaf (mathematics)
Famous quotes containing the word sheaves:
“A thousand golden sheaves were lying there,
Shining and still, but not for long to stay—
As if a thousand girls with golden hair
Might rise from where they slept and go away.”
—Edwin Arlington Robinson (1869–1935)