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:
“We say justly that the weak person is flat, for, like all flat substances, he does not stand in the direction of his strength, that is, on his edge, but affords a convenient surface to put upon. He slides all the way through life.... But the brave man is a perfect sphere, which cannot fall on its flat side and is equally strong every way.”
—Henry David Thoreau (18171862)
“What if it tempt you toward the flood, my lord,
Or to the dreadful summit of the cliff
That beetles oer his base into the sea,
And there assume some other horrible form
Which might deprive your sovereignty of reason,
And draw you into madness?”
—William Shakespeare (15641616)
“A man may see how this world goes with no eyes. Look with thine ears;
see how yond justice rails upon yond simple thief. Hark in thine ear: change places, and handy-dandy, which is the justice, which is the thief?”
—William Shakespeare (15641616)
“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)