Let $C$ be a smooth projective curve of genus $g\geq 1$ over an algebraically closed field. Let $\mathcal{M}$ be a line bundle with $deg \mathcal{M}\geq 2g -1$. Let $T$ be torsion and denote by $U$ the kernel of the map $\mathcal{O}^n\to T$ ( Edit: where $n=H^0(T)$ ). $\mathcal{M}$ is non-special, so $H^1(\mathcal{M})=0$.
I am trying to understand that $H^1(\mathcal{M})=0$ implies $H^1(M\otimes U)$ vanishes. Any help is appreciated,
I got this from the proof of lemma 7 in 'Orlov:Remarks on Generators and Dimension of Triangulated Categories, http://arxiv.org/abs/0804.1163