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determinant of cohomology of symplectic local systems

Let $X$ be an algebraic curve over $\mathbb C$ and let $E$ be a symplectic local system on $X$. For simplicity let us assume that $H^0(E)=H^2(E)=0$. Then $H^1(E)$ has a symmetric bilinear form and thu …
Alexander Braverman's user avatar