different types of K theory - ag.algebraic geometry - MathOverflow
mathoverflow.net
Algebraic K-theory sits at the crossroads of algebra, geometry, and topology — and this deep-dive into its competing variants reveals why mathematicians can't agree on a single framework.
Algebraic K-TheoryCategory TheoryHomotopy TheoryGrothendieck Group
Theory Briefing
- Srinivas's book and Thomason-Trobaugh's foundational paper introduce multiple competing formulations of algebraic K-theory, each capturing different geometric data.
- K-theory classifies vector bundles and projective modules, making it a unifying language across algebraic geometry, number theory, and topology.
- The existence of distinct K-theory variants — G-theory, KH-theory, and more — reflects deep structural tensions in how mathematicians model algebraic spaces.