Unformatted text preview: first is the Hodge filtration (1.4.1), (the "bestial" one in the terminology of ). The second is the one, noted Z<o and called "canonical" in , which is defined by K" if n<p (188.8.131.52) Z<p(K)= Ker(d) if n=p = tO if n>p. The spectral sequence defined by this filtration (184.108.40.206) ~<=.Ef'"=RP+qf.(gr~.K) ~RP+qf,(K) is the d~calage (cf. , 1.3.3) of the "second spectral sequence of hyper- cohomology" (220.127.116.11) ,,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 (18.104.22.168) ~ < ,E~' q - lla.~r + 1 for each integer r> 1 (cf. ). 2.3. The Conjugate Spectral Sequence (2.3.0) Recall that the entire "second spectral sequence" of hyper- cohomology (22.214.171.124) E~'q=RPf, (~q(f21,/s(log D))) =~ RP+qf,(t2]/s(log D))...
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- Fall '11
- Category theory, Isomorphism, spectral sequence, Epimorphism, hyperc ohomology