Descent in algebraic K-theory and a conjecture of Ausoni-Rognes

Autor: Niko Naumann, Akhil Mathew, Justin Noel, Dustin Clausen

Publikováno v: Clausen, D, Mathew, A, Naumann, N & Noel, J 2020, ' Descent in algebraic K-theory and a conjecture of Ausoni-Rognes ', Journal of the European Mathematical Society, vol. 22, no. 4, pp. 1149-1200 . https://doi.org/10.4171/JEMS/942

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 $K(A) \to K(B)^{hG}$ is to being an equivalence, i.e., how

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https://curis.ku.dk/portal/da/publications/descent-in-algebraic-ktheory-and-a-conjecture-of-ausonirognes(c28ca87c-85e2-427a-b5eb-ac848eda9b01).html

Rigidity in equivariant algebraic $K$-theory

Autor: Charanya Ravi, Niko Naumann

Publikováno v: Ann. K-Theory 5, no. 1 (2020), 141-158

If [math] is a henselian pair with an action of a finite group [math] and [math] is an integer coprime to [math] such that [math] , then the reduction map of mod- [math] equivariant [math] -theory spectra ¶ K G ( R ) ∕ n → ≃ K G ( R ∕ I ) �

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The Balmer spectrum of the equivariant homotopy category of a finite abelian group

Autor: Markus Hausmann, Nathaniel Stapleton, Justin Noel, Niko Naumann, Tobias Barthel, Thomas Nikolaus

Publikováno v: Inventiones Mathematicae

For a finite abelian group $A$, we determine the Balmer spectrum of $\mathrm{Sp}_A^{\omega}$, the compact objects in genuine $A$-spectra. This generalizes the case $A=\mathbb{Z}/p\mathbb{Z}$ due to Balmer and Sanders \cite{Balmer-Sanders}, by establi

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Existence and uniqueness of $$E_{\infty }$$ E ∞ structures on motivic $$K$$ K -theory spectra

Autor: Niko Naumann, Paul Arne Østvær, Markus Spitzweck

Publikováno v: Journal of Homotopy and Related Structures. 10:333-346

We show that algebraic \({\textit{K}}\)-theory \(\mathsf {KGL}\), the motivic Adams summand \(\mathsf {ML}\) and their connective covers acquire unique \(E_{\infty }\) structures refining naive multiplicative structures in the motivic stable homotopy

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https://doi.org/10.1007/s40062-013-0062-3

Some complements to the Lazard isomorphism

Autor: Guido Kings, Annette Huber, Niko Naumann

Publikováno v: Compositio Mathematica. 147:235-262

Lazard showed in his seminal work "Groupes analytiques $p$-adiques" that for rational coefficients continuous group cohomology of $p$-adic Lie-groups is isomorphic to Lie-algebra cohomology. We refine this result in two directions: firstly we extend

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https://doi.org/10.1112/s0010437x10004884