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60
N.M. Katz:
The corresponding spectral sequence in locally free (gs.nmodules of
finite rank
tyn,k+n__
nknIr~an
Flan/~'an)
Wt'I (an)

(~
DR ~xlil n,.
.n L"i~/~
!
(4.1.1.2)
i,<.
.<i,
Rkf,"((a~/s(log
O)) a")
is of formation compatible with arbitrary change of base S' ~ S an in the
category of analytic spaces, thanks to (4.0.3).
The canonical morphism of spectral sequences
(4.1.1.3)
(4.0.1.6)~ (4.1.1.2)
induces horizontal (for the GaussManin connections (4.0.2)) morphisms
(4.1.1.4)
E,  (gs~, ~ Er(an).
d)s
In fact, the morphisms (4.1.1.4) are all
isomorphisms,
because source
and target are locally free (_gsa,modules of finite rank of formation com
patible with arbitrary change of base, and because (by GAGA) the
morphism
(4.1.1.3) of spectral sequences is an isomorphism
when
S=Spec(C).
Thus the analytic spectral sequence (4.1.1.2) gives rise, via the functor
"germs of local horizontal sections" (which is an equivalence of categories
between coherent sheaves on
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 Fall '11
 NormanKatz

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