Unformatted text preview: first is the Hodge filtration (1.4.1), (the "bestial" one in the terminology of [8]). The second is the one, noted Z<o and called "canonical" in [8], which is defined by K" if n<p (2.2.2.1) Z<p(K)= Ker(d) if n=p = tO if n>p. The spectral sequence defined by this filtration (2.2.2.2) ~<=.Ef'"=RP+qf.(gr~.K) ~RP+qf,(K) is the d~calage (cf. [8], 1.3.3) of the "second spectral sequence of hyper cohomology" (2.2.2.3) ,,E~ 'q = RP f. (~ffq (K)) => R p +q f. (K), which by definition means that we have isomorphisms, compatible with the dr and with the standard isomorphism Er+, ~H(E, dr), ~, l~q+2p,p (2.2.2.4) ~ < ,E~' q  lla.~r + 1 for each integer r> 1 (cf. [8]). 2.3. The Conjugate Spectral Sequence (2.3.0) Recall that the entire "second spectral sequence" of hyper cohomology (2.3.0.1) E~'q=RPf, (~q(f21,/s(log D))) =~ RP+qf,(t2]/s(log D))...
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 Fall '11
 NormanKatz

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