We take a fresh look at the relationship between
-regularity
and regularity of schemes, proving two results in this direction. First, we show that
-regular
affine algebras over fields of characteristic zero are normal. Second, we improve on Vorst’s
-regularity
bound in the case of local complete intersections; this is related to recent work on
higher du Bois singularities.
Keywords
algebraic $K\mkern-2mu$-theory, cyclic homology, du Bois
complex, algebraic surfaces