Examples of finite free complexes of small rank and small homology

This work concerns finite free complexes over commutative noetherian rings, in particular over group algebras of elementary abelian groups. The main contribution is the construction of complexes such that the total rank of their underlying free modules, or the total length of their homology, is less than predicted by various conjectures in the theory of transformation groups and in local algebra.Comment: 13 pages. Version 2 is a significant revision of the first one. This paper will appear in Acta Mathematic

The equivariant K-theory of toric varieties

This paper contains two results concerning the equivariant K-theory of toric varieties. The first is a formula for the equivariant K-groups of an arbitrary affine toric variety, generalizing the known formula for smooth ones. In fact, this result is established in a more general context, involving the K-theory of graded projective modules. The second result is a new proof of a theorem due to Vezzosi and Vistoli concerning the equivariant K-theory of smooth (not necessarily affine) toric varieties.Comment: 12 page

Weight zero motivic cohomology and the general linear group of a simplicial ring

AbstractUsing elementary observations concerning the simplicial group obtained by applying the functor GL to a connected simplicial ring, we obtain computations of the weight zero pieces of two proposed filtrations of the K-theory space of a regular ring