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Operations on filtered / graded vector spaces via $\mathbb{A}^1 / \mathbb{G}_m$

For question 1, by the Rees construction the corresponding quasi-coherent sheaf is the graded $k[t]$-vector space $V\otimes k[t]$. This is simply the quasi-coherent sheaf $V\otimes_k\mathcal O_{\...
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