ag.algebraic geometry - lisse sheaf on complex varieties

Dear Shenghao, If you really do mean a lisse sheaf on the etale site of $X$, then it doesn't make sense a priori to evaluate it on analytic open subsets of $X(mathbb C)$, since these are not in the etale site of the algebraic variety $X$. However, $F$ corresponds to a representation of the (profinite) etale $pi_1$ of $X$, which in turn is the profinite completion of the
topological $pi_1$ of $X(mathbb C)$. So there is a corresponding locally constant (in the analytic topology) $mathbb Z_{ell}$
sheaf on $X(mathbb C)$, which, being locally constant, will be constant on sufficiently small analytic open subsets.

• Next nt.number theory - Perron-Frobenius "inverse eigenvalue problem"
• Previous mp.mathematical physics - Where does a math person go to learn statistical mechanics?