An application of a theorem of Gabber on alterations to algebraic K-theory via a new Grothendieck topology.
Vortrag von Dr. Shane Kelly
Sprecher eingeladen von: Prof. Dr. Andrew Kresch
Datum: 02.05.12 Zeit: 10.15 - 11.00 Raum: Y27H12
The assumption that the base field admits resolution of singularities litters Voevodsky's work on motives. While we still don't have resolution of singularities in positive characteristic, in 1996 de Jong provided a substitute if we are willing to work with rational coefficients. More recently, Gabber has proven a theorem in the same spirit to de Jong which allows us to work with Z[1/p] coefficients. We discuss how this theorem of Gabber can be applied to provide a partial response to a conjecture of Weibel on the vanishing of algebraic K-theory. If time permits, we will also mention a result of Suslin now valid in positive characteristic which compares étale cohomology and Bloch's Higher Chow groups.