60 N.M. Katz: The corresponding spectral sequence in locally free (gs.n-modules of finite rank ty-n,k+n__ nk-nIr~an Flan/~'an) Wt-'I (an) -- (~ DR ~xlil n,..n L"i~/~ ! (184.108.40.206) 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 (220.127.116.11) (18.104.22.168)--~ (22.214.171.124) induces horizontal (for the Gauss-Manin connections (4.0.2)) morphisms (126.96.36.199) E, | (gs~, ~ Er(an). d)s In fact, the morphisms (188.8.131.52) 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 (184.108.40.206) of spectral sequences is an isomorphism when S=Spec(C). Thus the analytic spectral sequence (220.127.116.11) gives rise, via the functor "germs of local horizontal sections" (which is an equivalence of categories between coherent sheaves on
This is the end of the preview. Sign up
access the rest of the document.