Let K/k be a finitely generated field extension. Then Ω_{K/k} and H_{1}(L_{K/k}) are finite dimensional and trdeg_{k}(K) = dim_{K} Ω_{K/k} – dim_{K} H_{1}(L_{K/k}). See Tag 07E1.

_{K/k} and H_{1}(L_{K/k}) are finite dimensional and trdeg_{k}(K) = dim_{K} Ω_{K/k} – dim_{K} H_{1}(L_{K/k}). See Tag 07E1.