Suppose $k$ is a number field. I want to compute $H^\ast({\mathbb P}^n_k,\mu_l^{\otimes r})$ where $l,r\in {\mathbb N}$. I know that Milne has some computations, but he assumes throughout that his field is ${\mathbb C}$. I want to know if it differs when $k$ is number field.
Disclaimer: This is not a homework problem. However, I am just a starter when it comes to the etale world. Any hints/comments will be appreciated. Thanks.