  Let $\mathbb K$ be a field of characteristic 0, let $S$ be a complete local
ring with coefficient field $\mathbb K$, let $\mathbb K[[x_1,\dots,x_n]]$ be
the ring of formal power series in variables $x_1,\dots, x_n$ with coefficients
from $\mathbb K$, let $\mathbb K[[x_1,\dots,x_n]]\to S$ be a $\mathbb
K$-algebra surjection and let $E_\bullet^{\bullet,\bullet} $ be the associated
Hodge-de Rham spectral sequence for the computation of the de Rham homology of
$S$. Nicholas Switala proved that this spectral sequence is independent of the
surjection beginning with the $E_2$ page, and the groups $E^{p,q}_2$ are all
finite-dimensional over $\mathbb K$.
  In this paper we extend this result to affine varieties. Namely, let $Y$ be
an affine variety over $\mathbb K$, let $X$ be a non-singular affine variety
over $\mathbb K$, let $Y\subset X$ be an embedding over $\mathbb K$ and let
$E_\bullet^{\bullet,\bullet} $ be the associated Hodge-de Rham spectral
sequence for the computation of the de Rham homology of $Y$. Then this spectral
sequence is independent of the embedding beginning with the $E_2$ page, and the
groups $E^{p,q}_2$ are all finite-dimensional over $\mathbb K$.
