Unformatted text preview: (126.96.36.199.1) is degenerate at El, all of its terms E( 'q, E~; ~ are locally free, and its formation commutes with arbitrary change of base S' -~ S. (188.8.131.52.2) If S is any reduced and irreducible scheme whose generic point is of characteristic zero, there exists a non-void Zariski open set q/in S over which the assertions of (184.108.40.206.1) are valid. We conclude this section by stating explicitly a very useful corollary of (220.127.116.11). (18.104.22.168) Corollary. Hypotheses as in (22.214.171.124), fix an integer n>=O, and suppose that M~=R"f,(O~cls(log D)) is an Os-submodule stable under the Gauss-Manin connection, i.e., that (126.96.36.199.1) V(M) c 0~1T | M. (We then say that M is horizontal.) Let us define the induced Hodge filtration of M, Fi(M), by (188.8.131.52.2) F' (M)= M c~ F i R"f, (f2~ls (log D))....
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- Fall '11
- Algebraic geometry, Zariski topology, Gauss-Manin conn ection, =~ RP +qf