Frobenius and Verschiebung for $K$-theory of endomorphisms
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911045480611840 |
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| author | Agarwal, Sanjana Campbell, Jonathan Manco, Diego Ponto, Kate Sun, Zhonghui |
| author_facet | Agarwal, Sanjana Campbell, Jonathan Manco, Diego Ponto, Kate Sun, Zhonghui |
| contents | 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 |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05956 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Frobenius and Verschiebung for $K$-theory of endomorphisms Agarwal, Sanjana Campbell, Jonathan Manco, Diego Ponto, Kate Sun, Zhonghui K-Theory and Homology Algebraic Topology Category Theory 19A99, 18F30 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 |
| title | Frobenius and Verschiebung for $K$-theory of endomorphisms |
| topic | K-Theory and Homology Algebraic Topology Category Theory 19A99, 18F30 |
| url | https://arxiv.org/abs/2507.05956 |