If $k$ is a Noetherian ring, then do the Kahler forms of a smooth affine $k$-algebra of dimension $d$ vanish above $d$?
I mean is: $\Omega^{d+1}_{A|k}\cong 0$?
2026-04-06 08:08:37.1775462917
Kahler forms of a smooth affine algebra vanish eventually?
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This follows precisely from the fact that $\Omega_{A/k}^1$ is locally free of rank $d$ (by smoothness). So, locally $\wedge^{d+1}\Omega_{A^k}^1$ is locally zero, and so globally zero.