We take a fresh look at the relationship between K-theory
and geometry, specifically K-regularity and regularity of
schemes, proving two new results:
First, we show that K_2-regular affine algebras over fields
of characteristic zero are normal.
Second, we improve on Vorst's "K-regularity-implies-regular"
bound in the case of local complete intersections;
this is related to recent work on higher du Bois singularities.