Jump to content

Weibel's conjecture

From Wikipedia, the free encyclopedia

In mathematics, Weibel's conjecture gives a criterion for vanishing of negative algebraic K-theory groups. The conjecture was proposed by Charles Weibel (1980) and proven in full generality by Kerz, Strunk & Tamme (2018) using methods from derived algebraic geometry. Previously partial cases had been proven by Morrow (2016), Kelly (2014), Cisinski (2013), Geisser & Hesselholt (2010), and Cortiñas et al. (2008).

Statement of the conjecture

[edit]

Weibel's conjecture asserts that for a Noetherian scheme X of finite Krull dimension d, the K-groups vanish in degrees < −d:

and asserts moreover a homotopy invariance property for negative K-groups

References

[edit]
  • Weibel, Charles (1980), "K-theory and analytic isomorphisms", Inventiones Mathematicae, 61 (2): 177–197, doi:10.1007/bf01390120