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This question is motivated by this recent question. Suppose $R$ is commutative, Noetherian ring and $M$ a finitely generated $R$-module. Let $FD(M)$ and $PD(M)$ be the shortest length of free and ...

Let $K$ be a non-algebraically closed field of characteristic $0$ and $X_K$ a smooth, projective, geometrically connected curve defined over $K$. If $F$ is a stable locally free sheaf on $X_K$, is it ...