• 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…

## References

SHOWING 1-10 OF 23 REFERENCES

### Excision in cyclic homology and in rational algebraic $K$-theory

(for a precise definition, see ?1 below). By replacing everywhere K*( ) by K*( ) ? Q, one obtains the corresponding notion in rational algebraic K-theory. The above definition has an obvious

### ALGEBRAIC K-THEORY OF SPACES I

The algebraic K–theory of spaces is a variant, invented by F. Waldhausen in the late 1970’s, of the standard algebraic K–theory of rings. Until that time, applications of algebraic K–theory to

### Generators in formal deformations of categories

• Mathematics
Compositio Mathematica
• 2018
In this paper we use the theory of formal moduli problems developed by Lurie in order to study the space of formal deformations of a $k$ -linear $\infty$ -category for a field $k$ . Our main result

### Relative Chern Characters for Nilpotent Ideals

• Mathematics
• 2009
When A is a unital ring, the absolute Chern character is a group homomorphism Ch* : K*(A) ? HN*(A), going from algebraic K-theory to negative cyclic homology. There is also a relative version,

### Infinitesimal cohomology and the Chern character to negative cyclic homology

• Mathematics
• 2007
There is a Chern character from K-theory to negative cyclic homology. We show that it preserves the decomposition coming from Adams operations, at least in characteristic zero.

### Higher Algebra

AbstractTHIS new “Higher Algebra” will be examined with great interest by all teachers and serious students of mathematics. A book of this type is certainly needed at the present time, and the one

### Tsygan: Homology of matrix Lie algebras over rings and the Hochschild homology

• Uspekhi Mat. Nauk, 38(2(230)) pp.217–218,
• 1983