4,060 research outputs found
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
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