  Let $(A,\mathfrak{m}, k=A/\mathfrak{m})$ be a noetherian local ring. Then it
is equivalent $n = \dim A = \dim_k \mathfrak{m}/\mathfrak{m}^2$ and
$\mathrm{Tor}^A_i(k,k) = 0$ for all $i \gg 0$. The article gives a proof with
the change-of-ring spectral sequence in the derived category form.
