Unformatted text preview: (1.4.1.7.1) 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. (1.4.1.8.2) If S is any reduced and irreducible scheme whose generic point is of characteristic zero, there exists a nonvoid Zariski open set q/in S over which the assertions of (1.4.1.8.1) are valid. We conclude this section by stating explicitly a very useful corollary of (1.4.1.7). (1.4.1.9) Corollary. Hypotheses as in (1.4.1.7), fix an integer n>=O, and suppose that M~=R"f,(O~cls(log D)) is an Ossubmodule stable under the GaussManin connection, i.e., that (1.4.1.9.1) 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 (1.4.1.9.2) F' (M)= M c~ F i R"f, (f2~ls (log D))....
View
Full Document
 Fall '11
 NormanKatz
 Algebraic geometry, Zariski topology, GaussManin conn ection, =~ RP +qf

Click to edit the document details