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Geometric Frobenius on $\ell$-adic cohomology

Let $X$ be a smooth projective variety over a finite field $k$, and $F$ the geometric Frobenius on $H^*_{et}(X_{k^{sep}}, \mathbf{Z}_{\ell})$.

Is $F$ only rationally bijective, or integrally bijective too?

ag.algebraic-geometry arithmetic-geometry etale-cohomology

asked Mar 31, 2018 at 18:16

user120812