I know a local system is a locally constant constant sheaf. But why does a local system on the topological space $X$ correspond to $\tilde{X}\times_G V$, where $G$ is the fundamental group of $X$, $\tilde{X}$ is the universal covering space of $X$, and $V$ is a $G$-module? How do you recover the locally free sheaf from $\tilde{X} \times_G V$?
What local system really is
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algebraic-topology
coherent-sheaves