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$\mathscr Coh_{X|S} $ is algebraic and of finite type
Let $S$ be a Noetherian scheme and $X$ a projective $S$-scheme.
Reading Laumon-Moret--Bailly's "Champs Algebriques", Theorem 4.6.2.1:
$ \mathscr Coh_{X|S} $ and $ \mathscr Fib_{X|S,r} $ are ...
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