K-theory and derived equivalences
Daniel Dugger (University of Oregon), Brooke Shipley (Purdue, University)
TL;DR
This paper proves that derived equivalences between rings imply isomorphic algebraic K-theory, extending similar results to G-theory and certain abelian categories, highlighting deep connections between categorical and algebraic invariants.
Contribution
It establishes that derived equivalences preserve algebraic K-theory and G-theory for rings and broad classes of abelian categories, revealing new invariants under categorical equivalences.
Findings
Derived equivalence implies isomorphic algebraic K-theory.
Similar results hold for G-theory.
Applicable to a wide class of abelian categories.
Abstract
We show that if two rings have equivalent derived categories then they have the same algebraic K-theory. Similar results are given for G-theory, and for a large class of abelian categories.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra