Flat Base Change For Quasi-coherent Sheaves
The base change holds for a quasi-coherent sheaf (on ), provided that the map f is flat (together with a number of technical conditions: g needs to be a separated morphism of finite type, the schemes involved need to be Noetherian).
Read more about this topic: Base Change
Famous quotes containing the words flat, base, change and/or sheaves:
“Out in Hollywood, where the streets are paved with Goldwyn, the word sophisticate means, very simply, obscene. A sophisticated story is a dirty story. Some of that meaning was wafted eastward and got itself mixed up into the present definition. So that a sophisticate means: one who dwells in a tower made of a DuPont substitute for ivory and holds a glass of flat champagne in one hand and an album of dirty post cards in the other.”
—Dorothy Parker (18931967)
“Were I as base as is the lowly plain,
And you, my Love, as high as heaven above,
Yet should the thoughts of me, your humble swain,
Ascend to heaven in honour of my love.”
—Joshua Sylvester (15611618)
“Revolutions demand enormous sacrifices and, at the same time, create a new need to change the world again.”
—Friedrich Dürrenmatt (19211990)
“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 (18691935)