Let $k$ be an algebraically closed field. Let $V$ be a smooth projective variety over $k$. For a map $\phi:V\to V$, do the coefficients of the characteristic polynomial of $\phi^*:H^ i_{dR}(V/k)\to H^ i_{dR}(V/k)$ lie in the prime subfield of $k$?
2 of 2
edited title
Coefficients of the characteristic polynomial of the map on algebraic de Rham cohomology
user145520