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4 hours ago comment added Jason Starr Let $I$ be any ideal sheaf on $\mathcal{C}_{\mathbb{F}_p}$ such that $I^2$ is the zero ideal sheaf. Denote by $\mathcal{C}'_{\mathbb{F}_p}$ the closed subscheme of $\mathcal{C}_{\mathbb{F}_p}$ with ideal sheaf $I$. There is a long exact sequence: $H^1(\mathcal{C}_{\mathbb{F}_p},I)\to \text{Pic}(\mathcal{C}_{\mathbb{F}_p})\to \text{Pic}(\mathcal{C}'_{\mathbb{F}_p})\to 0.$
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S 9 hours ago history asked James Rawson CC BY-SA 4.0