Algebraic K-theory, cohomotopy K-groups, and Koszul duality

2026/05/06 by Xiaojun Chen, Farkhod Eshmatov, Maozhou Huang · 1 voice
Mathematics · #math.KT #math.RA

paper · pdf

Abstract

Let A be an augmented differential graded algebra over a field k of characteristic zero, and let A^!=RHom_A(k,k) be its Koszul dual algebra. Blumberg and Mandell showed that, under some finiteness conditions of A, the derived Koszul duality provides an equivalence between the K-theory K(thick_A(k)) of the triangulated thick subcategory generated by k and the K-theory K(A^!) of the derived category of perfect A^!-modules. Combining this equivalence with the Jones-Goodwillie Chern character and the Jones-McCleary isomorphism, we obtain that the K-groups K_n(thick_A(k)) are a concrete candidate for Loday's conjectural contravariant K-groups.

Citations

• Derived Koszul Duality and Involutions in the Algebraic K-Theory of Spaces
• On differential graded categories
• Duality in algebra and topology
• Koszul Duality Patterns in Representation Theory
• Algebraic K-theory of spaces

Discussions

• Xiaojun Chen, Farkhod Eshmatov, Maozhou Huang: Algebraic $K$-theory, cohomotopy $K$-groups, and Koszul duality https://arxiv.org/abs/2605.05128 https://arxiv.org/pdf/2605.05128 https://arxiv.org/html/ [bsky, 0 points, 0 comments]

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