The tangent complex of K-theory
| Autor: | Benjamin Hennion |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Functor General Mathematics Cyclic homology Deformation theory K-Theory and Homology (math.KT) Field (mathematics) K-theory Mathematics::Algebraic Topology Morphism Mathematics::K-Theory and Homology Mathematics::Category Theory Mathematics - K-Theory and Homology FOS: Mathematics Algebraic Topology (math.AT) Canonical map Mathematics - Algebraic Topology Abelian group Mathematics |
| Zdroj: | Journal de l’École polytechnique — Mathématiques. 8:895-932 |
| ISSN: | 2270-518X |
| DOI: | 10.5802/jep.161 |
| Popis: | We prove that the tangent complex of K-theory, in terms of (abelian) deformation problems over a characteristic 0 field k, is cyclic homology (over k). This equivalence is compatible with the $\lambda$-operations. In particular, the relative algebraic K-theory functor fully determines the absolute cyclic homology over any field k of characteristic 0. We also show that the Loday-Quillen-Tsygan generalized trace comes as the tangent morphism of the canonical map $BGL_\infty \to K$. The proof builds on results of Goodwillie, using Wodzicki's excision for cyclic homology and formal deformation theory \`a la Lurie-Pridham. Comment: 36 pages. Final version. To appear in Journal de l'\'Ecole Polytechnique |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|