Mathematics – K-Theory and Homology
Scientific paper
2001-04-17
Mathematics
K-Theory and Homology
Final version, to appear in K-Theory
Scientific paper
A natural higher K-theoretic analogue of the triviality of vector bundles on affine toric varieties is the conjecture on nilpotence of the multiplicative action of the natural numbers on the K-theory of these varieties. This includes both Quillen's fundamental result on K-homotopy invariance of regular rings and the stable version of the triviality of vector bundles on affine toric varieties. Moreover, it yields a similar behavior of not necessarily affine toric varieties and, further, of their equivariant closed subsets. The conjecture is equivalent to the claim that the relevant admissible morphisms of the category of vector bundles on an affine toric variety can be supported by monomials not in a non-degenerate corner subcone of the underlying polyhedral cone. We prove that one can in fact eliminate all lattice points in such a subcone, except maybe one point. The elimination of the last point is also possible in 0 characteristic if the action of the big Witt vectors satisfies a very natural condition. A partial result on this in the arithmetic case provides first non-simplicial examples -- actually, an explicit infinite series of combinatorially different affine toric varieties, verifying the conjecture for all higher groups simultaneously.
No associations
LandOfFree
Higher K-theory of toric varieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Higher K-theory of toric varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Higher K-theory of toric varieties will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-484281