Unformatted text preview: is/J+", whence (18.104.22.168) F i (L" In]) = (F i +" (L')) [n]. Applying F ~ to the exact sequence (22.214.171.124), we obtain the exact sequence 0 -~ (f* (12~/r) | F i-1 (12],/s (log D))) [ - 1 ] (126.96.36.199) -~ 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 (188.8.131.52) and (184.108.40.206) "fit together" to form a commutative diagram Rqf,(O]ls(log D))--E-~ v 12Xs/r| (2~/s(log D)) (220.127.116.11) | Rqf, (F *(O]/s (log D))) _~00]/r | Rqf, (U- 1 (O]/s(log D))). Thus we find: (18.104.22.168) PrOlmSition (Griffith's Transversality Theorem). The Gauss- Manin connection respects the Hodge filtration up to a shift of one, i.e. (22.214.171.124.1) 17(FiR~f,(g2]/s(log O))) =f2xs/r| D)))....
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- Fall '11
- Homological algebra, exact sequence, short exact sequence, Commutative diagram, N.M. Katz