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 (1893–1967)
“And all the popular statesmen say
That purity built up the State
And after kept it from decay;
Admonish us to cling to that
And let all base ambition be,
For intellect would make us proud....”
—William Butler Yeats (1865–1939)
“This is the end, the redemption from Wilderness, way for the
Wonderer, House sought for All, black handkerchief washed clean by
weeping—page beyond Psalm—Last change of mine and Naomi—to Gods perfect Darkness—Death, stay thy phantoms!”
—Allen Ginsberg (b. 1926)
“Being young you have not known
The fool’s triumph, nor yet
Love lost as soon as won,
Nor the best labourer dead
And all the sheaves to bind.”
—William Butler Yeats (1865–1939)