Algebraic K-theory can detect when a quasi-projective variety is smooth; for the variety Spec R of a commutative ring R, it is the comparison of K_n(R) with K_n(R[t]) for n near dim(R); in general we need to compare with the K-theory of an ample line bundle in the same range. The methods are essentially sheaf cohomology, little about K-theory is assumed.