Weibel's conjecture, proposed by Charles Weibel in 1980, gives a criterion for the vanishing of negative algebraic K-theory groups. It was proven in full generality by Moritz Kerz, Florian Strunk and Georg Tamme in 2018 using methods from derived algebraic geometry, after partial cases had been established by several other mathematicians over the preceding decade.
Facts
StatementFor a Noetherian scheme X of finite Krull dimension d, the algebraic K-groups of X vanish in degrees less than negative d, and the negative K-groups satisfy a homotopy invariance property, meaning the K-group in degree i of X equals the K-group in degree i of X times affine r-space for every i less than or equal to negative d. 1 Proposed Year Progress Toward ResolutionThe conjecture was proven in full generality in 2018 by Moritz Kerz, Florian Strunk and Georg Tamme using methods from derived algebraic geometry, after partial cases had been established earlier by Haesemeyer in 2004, Cortinas and coauthors in 2008, Geisser and Hesselholt in 2010, Cisinski in 2013, Kelly in 2014 and Morrow in 2016. 1 Classification
Resolution Status Chronology
Resolved Year Prize Status
Prize Status (category) Sources
1. Weibel's Conjecture (Wikipedia)
Statement of the conjecture section
Weibel's conjecture asserts that for a Noetherian scheme X of finite Krull dimension d, the K-groups vanish in degrees < -d
Introduction section, attribution sentence
The conjecture was proposed by Weibel (1980) and proven in full generality by Kerz, Strunk & Tamme (2018) using methods from derived algebraic geometry.
Introduction section, resolution sentence
proven in full generality by Kerz, Strunk & Tamme (2018) using methods from derived algebraic geometry
- Lead section
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