Base Change - Flat Base Change For Quasi-coherent Sheaves

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:

    They are not flat surfaces
    Having curved outlines.
    They are round
    Tapering toward the top.
    Wallace Stevens (1879–1955)

    Music is of two kinds: one petty, poor, second-rate, never varying, its base the hundred or so phrasings which all musicians understand, a babbling which is more or less pleasant, the life that most composers live.
    HonorĂ© De Balzac (1799–1850)

    I acknowledge that the balance I have achieved between work and family roles comes at a cost, and every day I must weigh whether I live with that cost happily or guiltily, or whether some other lifestyle entails trade-offs I might accept more readily. It is always my choice: to change what I cannot tolerate, or tolerate what I cannot—or will not—change.
    Melinda M. Marshall (20th century)

    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)