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Small changes in derham and cohomology

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aisejohan committed Nov 7, 2019
1 parent 801072a commit c99a0f682396c6cb8817a5f2d96226415bcba978
Showing with 2 additions and 3 deletions.
  1. +0 −2 cohomology.tex
  2. +2 −1 derham.tex
@@ -6516,8 +6516,6 @@ \section{Cohomology of filtered complexes}
complex of $\mathcal{O}_X$-modules. We can apply
Lemma \ref{lemma-spectral-sequence-filtered-object}
with $F^p\mathcal{F}^\bullet = \sigma_{\geq p}\mathcal{F}^\bullet$.
(If $\mathcal{F}^\bullet$ is bounded below we can use
Remark \ref{remark-spectral-sequence-filtered-object}.)
Then we get a spectral sequence
$$
E_1^{p, q} = H^{p + q}(X, \mathcal{F}^p[-p]) = H^q(X, \mathcal{F}^p)
@@ -562,7 +562,8 @@ \section{The Hodge filtration}
Cohomology, Lemma \ref{cohomology-lemma-spectral-sequence-filtered-object}
for $\Omega^\bullet_{X/S}$ viewed as a filtered complex of sheaves
is the same as the Hodge-to-de Rham spectral sequence constructed in
Section \ref{section-hdoge-to-de-rham}. Further the
Section \ref{section-hdoge-to-de-rham} by
Cohomology, Example \ref{cohomology-example-spectral-sequence-bis}. Further the
wedge product (\ref{equation-wedge}) sends
$\text{Tot}(\sigma_{\geq i}\Omega^\bullet_{X/S} \otimes_{p^{-1}\mathcal{O}_S}
\sigma_{\geq j}\Omega^\bullet_{X/S})$ into

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