Let $k$ be a perfect field of characteristic $p$, and $L$ be a finite extension of $k$. For a smooth projective variety $X$ defined over $k$, we denote the base change $X \times_k L$ by $X_L$. In this setting, is there an isomorphism of W(L)-module $ H^j(X,W\Omega^i_{X/k}) \otimes_{W(k)}W(L) \simeq H^j(X,W\Omega^i_{{X_L}/L}) $ for all $i,j$ ?
Add a comment
|