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Fix typo in derham
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aisejohan committed Jun 9, 2020
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Expand Up @@ -184,6 +184,7 @@ Matthias Kummerer
Manoj Kummini
Daniel Krashen
Oleksandr Kravets
Matt Larson
Brian Lawrence
Geoffrey Lee
Heejong Lee
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2 changes: 1 addition & 1 deletion derham.tex
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Expand Up @@ -1600,7 +1600,7 @@ \section{de Rham cohomology of projective space}
By the computation of the Hodge cohomology of $\mathbf{P}^n_A$ over $A$
done in Lemma \ref{lemma-hodge-cohomology-projective-space}
we see that the spectral sequence degenerates on the $E_1$ page.
In this way we see that $H^i_{dR}(\mathbf{P}^n_A/A)$ is a free
In this way we see that $H^{2i}_{dR}(\mathbf{P}^n_A/A)$ is a free
$A$-module of rank $1$ for $0 \leq i \leq n$ and zero else.
Observe that $c_1^{dR}(\mathcal{O}(1))^i \in H^{2i}_{dR}(\mathbf{P}^n_A/A)$
for $i = 0, \ldots, n$ and that for $i = n$ this element is the
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