Vanishing of negative $K$-theory in positive characteristic

Details Vanishing of negative $K$-theory in positive characteristic Vanishing of negative $K$-theory in positive characteristic

2011-12-21

arxiv.org/abs/1112.5206v3

Mathematics

Algebraic Geometry

* Made lemma 3.2 clearer. * Minor adjustments to the introduction. * Some typos. * Included missing reference to Haesemeyer

Scientific paper

We define a notion of presheaf with traces and use it to compare cdh cohomology and $\ell'$ cohomology where $\ell'$ refers to a topology in which Gabber's alterations are covers. We show that under certain hypotheses that are satisfied by homotopy invariant $K$-theory, the cdh and $\ell'$ sheafifications agree, and their cohomologies agree as well. As an application we use a recent preprint of Cisinski to prove that $K^B_n(X) \otimes \mathbb{Z}[1/p] = 0$ for $i < - \dim X$ where $X$ is a scheme essentially of finite type over a perfect field $k$ of characteristic $p > 0$ and $K^B$ is the $K$-theory of Bass-Thomason-Trobaugh.

Affiliated with

Also associated with

No associations

Rating

Vanishing of negative $K$-theory in positive characteristic 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 Vanishing of negative $K$-theory in positive characteristic, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Vanishing of negative $K$-theory in positive characteristic will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-305774