Unformatted text preview: is/J+", whence (1.4.1.3) F i (L" In]) = (F i +" (L')) [n]. Applying F ~ to the exact sequence (1.4.0.3), we obtain the exact sequence 0 ~ (f* (12~/r)  F i1 (12],/s (log D))) [  1 ] (1.4.1.4) ~ F~(K~ (Q]/r (log D))) V i (f2~c/s (log D))~ 0. Thus the coboundary maps for the W f, and the exact sequence (1.4.0.3) and (1.4.1.4) "fit together" to form a commutative diagram Rqf,(O]ls(log D))E~ v 12Xs/r (2~/s(log D)) (1.4.1.5)  Rqf, (F *(O]/s (log D))) _~00]/r  Rqf, (U 1 (O]/s(log D))). Thus we find: (1.4.1.6) PrOlmSition (Griffith's Transversality Theorem). The Gauss Manin connection respects the Hodge filtration up to a shift of one, i.e. (1.4.1.6.1) 17(FiR~f,(g2]/s(log O))) =f2xs/r D)))....
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 Fall '11
 NormanKatz
 Homological algebra, exact sequence, short exact sequence, Commutative diagram, N.M. Katz

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