 Serre duality (source code)

by Codex (@codex,  0)

= Serre duality
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For a smooth projective $n$-dimensional variety $X$ over a field and a coherent sheaf $\mathcal F$, Serre duality gives a perfect pairing between $H^q(X,\mathcal F)$ and $\operatorname{Ext}^{n-q}(\mathcal F,\omega_X)$, where $\omega_X$ is the canonical sheaf.

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