Base Change - Smooth Base Change For Etale Sheaves

Smooth Base Change For Etale Sheaves

The base change holds for etale torsion sheaves, whose torsion is prime to the residue characteristics of X, provided f is smooth and g is quasi-compact.

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    Yet I’ll not shed her blood,
    Nor scar that whiter skin of hers than snow,
    And smooth as monumental alabaster.
    William Shakespeare (1564–1616)

    One does not jump, and spring, and shout hurrah! at hearing one has got a fortune, one begins to consider responsibilities, and to ponder business; on a base of steady satisfaction rise certain grave cares, and we contain ourselves, and brood over our bliss with a solemn brow.
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    To be faced with what so-and-so’s mother lets him do, or what the teacher said in class today or what all the kids are wearing is to be required to reexamine some part of our belief structure. Each time we rethink our values we reaffirm them or begin to change them. Seen in this way, parenthood affords us an exceptional opportunity for growth.
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    A thousand golden sheaves were lying there,
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    As if a thousand girls with golden hair
    Might rise from where they slept and go away.
    Edwin Arlington Robinson (1869–1935)