Frobenius and Verschiebung for $K$-theory of endomorphisms
Sanjana Agarwal, Jonathan Campbell, Diego Manco, Kate Ponto, Zhonghui Sun
TL;DR
This paper extends the concepts of Frobenius and Verschiebung maps to the reduced K-theory of endomorphisms, demonstrating their properties in non-commutative settings and their compatibility with trace maps.
Contribution
It introduces Frobenius and Verschiebung maps for the reduced K-theory of twisted endomorphisms over non-commutative rings, expanding their applicability.
Findings
Frobenius and Verschiebung maps lift to reduced K-theory of endomorphisms
These maps behave as expected after applying the trace map
The work applies to modules over non-commutative rings
Abstract
We show that the Frobenius and Verschiebung maps that are fundamental to Witt vectors lift to the reduced K-theory of endomorphisms. In particular, we define Frobenius and Verschiebung maps for the reduced K-theory of twisted endomorphisms of modules over non commutative rings and show they have the expected behavior after applying the iterated trace map
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory