Unformatted text preview: (188.8.131.52) wE;"'k+"= Hk-R"(Di, n'"nDi./S)~ Rkf.(t2;x./s(logD)). il <'"<in (4.0.2) Proposition. The spectral sequence (184.108.40.206) is (naturally) a spectral sequence with cup-product in the category of quasi-coherent (gs-modules with integrable connection relative to T. This connection is the Gauss-Martin connection on the El terms and on the abutment. In particular, the W filtration on the Rkf,(Q}/s(logD)) is horizontal for the Gauss-Manin connection. Proof. The product structure in the spectral sequence results from (220.127.116.11). The action of the Gauss-Manin connection on the spectral sequence may be seen directly as follows. The question being local on S, we may suppose S affine. Choose an affine open covering of X by suf- ficiently small coordinatized open sets V v as in (3.4.1). The filtration W of f2~/s(logD) induces a filtration W on the Cech bicomplex of quasi-coherent (gs-modules (18.104.22.168) W~ C~ t2}/s(logD)) dN,, C~ W~f21/s(logO) )...
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This note was uploaded on 12/21/2011 for the course MAP 4341 taught by Professor Normankatz during the Fall '11 term at UNF.
- Fall '11