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:
“Man is a wingless animal with two feet and flat nails.”
—Plato (c. 427347 B.C.)
“Report of fashions in proud Italy,
Whose manners still our tardy-apish nation
Limps after in base imitation.”
—William Shakespeare (15641616)
“To suffer woes which Hope thinks infinite;
To forgive wrongs darker than Death or Night;
To defy Power, which seems Omnipotent;
To love, and bear; to hope, till Hope creates
From its own wreck the thing it contemplates;
Neither to change nor falter nor repent;
This, like thy glory, Titan! is to be
Good, great and joyous, beautiful and free;
This is alone Life, Joy, Empire and Victory.”
—Percy Bysshe Shelley (17921822)
“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)