Corpus ID: 221083370

# A descent view on Mitchell's theorem.

@article{Elmanto2020ADV,
title={A descent view on Mitchell's theorem.},
author={E. Elmanto and Denis Nardin and Lucy Yang},
journal={arXiv: K-Theory and Homology},
year={2020}
}
• Published 2020
• Mathematics
• arXiv: K-Theory and Homology
In this short note, we given a new proof of Mitchell's theorem that $L_{T\left(n\right)} K(Z) \cong 0$ for $n \geq 2$. Instead of reducing the problem to delicate representation theory, we use recently established hyperdescent technology for chromatically-localized algebraic K-theory.

#### References

SHOWING 1-10 OF 29 REFERENCES
Remarks on K(1)-local K-theory
• Mathematics
• 2020
We prove two basic structural properties of the algebraic $K$-theory of rings after $K(1)$-localization at an implicit prime $p$. Our first result (also recently obtained by Land--Meier--Tamme byExpand
Vanishing results for chromatic localizations of algebraic $K$-theory
• Mathematics
• 2020
We show that algebraic $K$-theory preserves $n$-connective $L_{n}^{f}$-equivalences between connective ring spectra, generalizing a result of Waldhausen for rational algebraic $K$-theory to higherExpand
Hyperdescent and étale K-theory
• Mathematics
• 2019
We study the etale sheafification of algebraic K-theory, called etale K-theory. Our main results show that etale K-theory is very close to a noncommutative invariant called Selmer K-theory, which isExpand
Topological cyclic homology, Handbook of homotopy theory
• 2019
Topological cyclic homology, Handbook of homotopy theory (Haynes Miller, ed.), CRC Press/Chapman
• 2019
Descent in algebraic $K$-theory and a conjecture of Ausoni-Rognes
• Mathematics
• 2016
Let $A \to B$ be a $G$-Galois extension of rings, or more generally of $\mathbb{E}_\infty$-ring spectra in the sense of Rognes. A basic question in algebraic $K$-theory asks how close the map \$K(A)Expand
Chromatic redshift
Notes for the author’s MSRI lecture in January 2014.
On the algebraic K-theory of the complex K-theory spectrum
Let p≥5 be a prime, let ku be the connective complex K-theory spectrum, and let K(ku) be the algebraic K-theory spectrum of ku. In this paper we study the p-primary homotopy type of the spectrumExpand
On motivic cohomology with Z/l -coefficients
In this paper we prove the conjecture of Bloch and Kato which relates Milnor’s K-theory of a field with its Galois cohomology as well as the related comparisons results for motivic cohomology withExpand
The homotopy limit problem for two-primary algebraic K-theory
• Mathematics
• 2005
Abstract We solve the homotopy limit problem for two-primary algebraic K-theory of fields, that is, the Quillen–Lichtenbaum conjecture at the prime 2.