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5 votes
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Enough injectives in the category of quasi-coherent sheaves on a stack

In the paper A functorial formalism for quasi-coherent sheaves on a geometric stack, Expo. Math. 33 (2015) 452–501, in Corollary 5.10 it is shown that $\mathrm{Qco}(X)$ is a Grothendieck category for …
Leo Alonso's user avatar
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1 vote
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Is any "relative support" for (complexes of) quasi-coherent sheaves known?

Perhaps what you need is an action of of a tt-category (in your case $D(R)$) on the category $D_{qc}(X)$ which gives a support in $S$ to quasi-coherent complexes over $X$. This is discussed with great …
Leo Alonso's user avatar
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3 votes
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Basics(?) about quasi-coherent modules on projective schemes

Question 1: The category $C$ is often described as the quotient $$grMod(A)/TN(A)$$ where we denote by $TN(A)$ we denote The subcategory of $grMod(A)$ of graded modules $M$ such that $I^n m= 0$ for $ …
Leo Alonso's user avatar
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