A remark on the invariance of K-theory under duality

2026/03/09 by Georg Lehner · 1 voice
Mathematics · #math.KT #math.AT

paper · pdf

Abstract

In this short remark, we explain that two examples of invariance under duality for a localizing invariant F hold purely formally when F is K-theory, whereas the general statement for arbitrary localizing invariants does not reduce to a formal statement. We record a counterexample to the claim that the universal localizing invariant is invariant under the operation of taking opposite categories, originally due to Tabuada.

Citations

• Localizing motives of Azumaya algebras
• K-theory and localizing invariants of large categories
• Higher traces, noncommutative motives, and the categorified Chern\n character
• Additive invariants of toric and twisted projective homogeneous varieties via noncommutative motives
• A universal characterization of higher algebraic K-theory

Discussions

• Georg Lehner: A remark on the invariance of $K$-theory under duality https://arxiv.org/abs/2603.08344 https://arxiv.org/pdf/2603.08344 https://arxiv.org/html/2603.08344 [bsky, 0 points, 0 comments]

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