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Dr. Katz DEq Homework Solutions 62

Dr. Katz DEq Homework Solutions 62 - 62 N.M Katz is an...

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62 N.M. Katz: is an isomorphism between its source and the subsheaf Rq f,(f2~c/~) v of germs of horizontal sections (for the Gauss-Manin connection) of Rq/, (f2~./~). Proof The proof is an exercise in the definition of the Gauss-Manin connection (cf. (1.4) and [-35]). We consider the Koszul filtration K (of. (1.4)) of the complex s2]~/c, and the corresponding spectral sequence for the functors R f, (4.1.2.1) Ef'q=RV+q f,(gr~ ~2~c/c)=~.RP+q f,((2~r/c). By (the analytic version of) (1.4.0.2), we have (4.1.2.2) Fp, ~- ov | Rqf, (f2}/y). L'I -- ~5~/C By definition of the Gauss-Manin connection (cf. [35]), the differential (4.1.2.3) is the mapping (4.1.2.4)
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