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Absolute purity for intersection cohomology

If $i:Z\hookrightarrow X$ is a closed embedding of codimension $c$, then $$i^*k_X\ =\ k_Z , \ \ \ i^!k_X\ \stackrel{(\star)}{=}\ k_Z[2c]$$ where $(\star)$ is true when $i$ is in addition regular. Here …
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