Lemma 15.34.2. Let $M/L/K$ be field extensions. Then the Jacobi-Zariski sequence

$0 \to H_1(L_{L/K}) \otimes _ L M \to H_1(L_{M/K}) \to H_1(L_{M/L}) \to \Omega _{L/K} \otimes _ L M \to \Omega _{M/K} \to \Omega _{M/L} \to 0$

is exact.

There are also:

• 2 comment(s) on Section 15.34: Cartier's equality and geometric regularity

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).