Unformatted text preview: 144tt operation (2.3.4.1.6) HW: F* s R"f, (d~x) ~ R"f, ((gx) is none other than the intersection (F~"on ~ F 1) (R"f, (f2~/s(log D))). (2.3.4.1.7) Corollary (Assumptions as in (2.3.2)). In order to have a direct sum decomposition (2.3.4.1.8) R"f,(f2~/s(log D)), ~ F ~ GFc"on it is necessary and sufficient that the HasseWitt operation (2.3.4.1.9) HW: F*s R"f,((~x)~ R"f, ff)x) be an isomorphism. Proof. Since the statements whose equivalence is asserted are both of the form "a certain homomorphism of locally free Smodules of finite rank is an isomorphism", and because the formation of these modules commutes with all changes of base S' * S, we are immediately reduced to the case in which S is the spectrum of a field K. The isomorphisms ~g (2.3.4.1.10) co~E~ 'b ~,~ F~*~E~ 'a...
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This note was uploaded on 12/21/2011 for the course MAP 4341 taught by Professor Normankatz during the Fall '11 term at UNF.
 Fall '11
 NormanKatz

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