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:
“On a flat road runs the well-trained runner,
He is lean and sinewy with muscular legs,
He is thinly clothed, he leans forward as he runs,
With lightly closed fists and arms partially raised.”
—Walt Whitman (1819–1892)
“The base of all artistic genius is the power of conceiving humanity in a new, striking, rejoicing way, of putting a happy world of its own creation in place of the meaner world of common days, of generating around itself an atmosphere with a novel power of refraction, selecting, transforming, recombining the images it transmits, according to the choice of the imaginative intellect. In exercising this power, painting and poetry have a choice of subject almost unlimited.”
—Walter Pater (1839–1894)
“The incessant repetition of the same hand-work dwarfs the man, robs him of his strength, wit, and versatility, to make a pin- polisher, and buckle-maker, or any other specialty; and presently, in a change of industry, whole towns are sacrificed like ant-hills, when cotton takes the place of linen, or railways of turnpikes, or when commons are inclosed by landlords.”
—Ralph Waldo Emerson (1803–1882)
“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)