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 GaussManin
connection)
of
Rq/, (f2~./~).
Proof
The proof is an exercise in the
definition
of the GaussManin
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 GaussManin connection (cf. [35]), the differential
(4.1.2.3)
is the mapping
(4.1.2.4)
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 Fall '11
 NormanKatz
 Algebraic Topology, Category theory, Sheaf, GaussManin connection

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