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arXiv · 2507.05956

Frobenius and Verschiebung for $K$-theory of endomorphisms

Sanjana Agarwal·Jonathan Campbell·Diego Manco·Kate Ponto·Zhonghui Sun
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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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Sanjana Agarwal, Jonathan Campbell, Diego Manco, Kate Ponto, Zhonghui Sun. 2025-07-08. Frobenius and Verschiebung for $K$-theory of endomorphisms. https://arxiv.org/abs/2507.05956

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