6
votes
1answer
504 views

Proper morphism sending coherent to coherent

Hello, Is there a proof that the push forward by a proper morphism of Noetherian schemes sends coherent sheaves to coherent ones, without passing in the argument through projective morphisms? Thank ...
3
votes
1answer
534 views

Quasi-coherent sheaves of O_X-algebras

Let $X$ be a quasi-compact scheme and let $\mathcal{A}$ be a quasi-coherent sheaf of $\mathcal{O}_X$-algebras on $X$. $X$ being quasi-compact, we can write $X = U_1 \cup \dots \cup U_n$ with each ...