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2 votes

Find a non-quasi-compact scheme s.t. all finitely generated + globally generated quasi-coher...

Warning. This does not answer the question. See the comments. Let $k$ be a field. For each $n\in\mathbb{N}$, let $X_n$ be a copy of $\mathrm{Spec}(k)$. Put $X:=\coprod_{n\in\mathbb{N}}X_n$. We view $\ …
Laurent Moret-Bailly's user avatar
8 votes
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Flatness on the formal plane from flatness on lines through the origin?

On $X=\mathrm{Spec}\,\mathbb{C}[[t,h]]$, choose an irreducible curve of degree $\geq2$ (e.g. $t^2=h$) and let $\eta$ be its generic point, $j:\eta\to X$ the inclusion. Then $\mathcal{F}:=j_*\mathcal{O …
Laurent Moret-Bailly's user avatar