Yes. Both cohomology and number of points are readily determined by looking at the Schubert cells (a cell of dimension k contributes one dimension to $H^k$, and $q^k$ to the point count) and they match.

In fact, it's very easy to check Weil's conjecture directly for any smooth variety which has a decomposition into cells.

Yes. Both cohomology and number of points are readily determined by looking at the Schubert cells (a cell of dimension k contributes one dimension to $H^{2k}$, and $q^k$ to the point count) and they match.

In fact, it's very easy to check Weil's conjecture directly for any smooth variety which has a decomposition into cells.

Yes. Both cohomology and number of points are readily determined by looking at the Schubert cells (a cell of dimension k contributes one dimension to $H^k$, and $q^k$ to the point count) and they match.

Yes. Both cohomology and number of points are readily determined by looking at the Schubert cells (a cell of dimension k contributes one dimension to $H^k$, and $q^k$ to the point count) and they match.

In fact, it's very easy to check Weil's conjecture directly for any smooth variety which has a decomposition into cells.