We study the local homology of Artin groups using weighted discrete Morse
theory. In all finite and affine cases, we are able to construct Morse
matchings of a special type (we call them "precise matchings"). The existence
of precise matchings implies that the homology has a square-free torsion. This
property was known for Artin groups of finite type, but not in general for
Artin groups of affine type. We also use the constructed matchings to compute
the local homology in all exceptional cases, correcting some results in the
literature
