• Corpus ID: 119120169

Tangent of K-theory

@article{Hennion2019TangentOK,
  title={Tangent of K-theory},
  author={Benjamin Hennion},
  journal={arXiv: K-Theory and Homology},
  year={2019}
}
We show that the relative algebraic K-theory functor fully determines the absolute cyclic homology over any field k of characteristic 0. More precisely, we prove that the tangent of K-theory, in terms of (abelian) deformation problems over k, is cyclic homology. As a consequence, any structure on K-theory is inherited by cyclic homology. We also show that the Loday-Quillen-Tsygan generalized trace comes as the tangent morphism of the canonical map $BGL_\infty \to K$ mapping a vector bundle to… 

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