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:
“The allurement that women hold out to men is precisely the allurement that Cape Hatteras holds out to sailors: they are enormously dangerous and hence enormously fascinating. To the average man, doomed to some banal drudgery all his life long, they offer the only grand hazard that he ever encounters. Take them away, and his existence would be as flat and secure as that of a moo-cow.”
—H.L. (Henry Lewis)
“Adolescence is a time when children are supposed to move away from parents who are holding firm and protective behind them. When the parents disconnect, the children have no base to move away from or return to. They arent ready to face the world alone. With divorce, adolescents feel abandoned, and they are outraged at that abandonment. They are angry at both parents for letting them down. Often they feel that their parents broke the rules and so now they can too.”
—Mary Pipher (20th century)
“How vigilant we are! determined not to live by faith if we can avoid it; all the day long on the alert, at night we unwillingly say our prayers and commit ourselves to uncertainties. So thoroughly and sincerely are we compelled to live, reverencing our life, and denying the possibility of change. This is the only way, we say; but there are as many ways as there can be drawn radii from one centre. All change is a miracle to contemplate; but it is a miracle which is taking place every instant.”
—Henry David Thoreau (18171862)
“Being young you have not known
The fools triumph, nor yet
Love lost as soon as won,
Nor the best labourer dead
And all the sheaves to bind.”
—William Butler Yeats (18651939)