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:
“You dont want a general houseworker, do you? Or a traveling companion, quiet, refined, speaks fluent French entirely in the present tense? Or an assistant billiard-maker? Or a private librarian? Or a lady car-washer? Because if you do, I should appreciate your giving me a trial at the job. Any minute now, I am going to become one of the Great Unemployed. I am about to leave literature flat on its face. I dont want to review books any more. It cuts in too much on my reading.”
—Dorothy Parker (18931967)
“I am sure my bones would not rest in an English grave, or my clay mix with the earth of that country. I believe the thought would drive me mad on my death-bed could I suppose that any of my friends would be base enough to convey my carcass back to her soil. I would not even feed her worms if I could help it.”
—George Gordon Noel Byron (17881824)
“... often in the heat of noonday, leaning on a hoe, looking across valleys at the mountains, so blue, so close, my only conscious thought was, How can I ever get away from here? How can I get to where they have books, where I can be educated? I worked hard, always waiting for something to happen to change things. There came a time when I knew I must make them happen; that no one would do anything about it for me. And I did.”
—Belinda Jelliffe (18921979)
“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)