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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.

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Obstruction theory for specializing perfect complexes?

I'm considering a problem around the moduli of perfect complexes. Let's consider a $X$ smooth proper over Spec($R$), $R$ is a DVR, $char=0$, equipped with a perfect complex $\mathcal F$ on $X_{K(R)}$. …
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