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Unformatted text preview: ~ I'P(S, (9*) dlog , Hi(S, f~s/r) (the left hand zero because F(S, (9*)=F(T, (9*) is annihilated by d log). The trace morphism (of. [15, 42]) defines a functorial isomorphism (7.4.0.2) H 1(S, Qs~/r) ~, a = F(T, (9r) (7.4.0.3) If P is a section of S/T, its image IPI is a divisor in S which is smooth over T. The inverse of its sheaf of ideals is an invertible sheaf on S, noted classically (gs([P]). If P1, .., Pr are sections, and n 1, . .., nr integers, we define the invertible sheaf (7.4.0.4) (9 s (Z n i [P~]) = (gs ([P1])174 ...  (9s ([P~]) The composite mapping trace (7.4.0.5) HI(S, (9,) dlog ) HI(S, ~r~IS/T) ~~,A allows us to attach to the class in Hi(S, (9*) of Os(Z ni [Pi]) an element of A, which is none other than the image in A of the integer 2; ni. Thus...
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 Fall '11
 NormanKatz

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