Unformatted text preview: 144tt operation (184.108.40.206.6) H-W: 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))). (220.127.116.11.7) Corollary (Assumptions as in (2.3.2)). In order to have a direct sum decomposition (18.104.22.168.8) R"f,(f2~/s(log D)), ~ F ~ GFc"on it is necessary and sufficient that the Hasse-Witt operation (22.214.171.124.9) H-W: 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 S-modules 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 (126.96.36.199.10) 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