We prove that $ T (n+ 1) $-localized algebraic $ K $-theory satisfies descent for $\pi $-finite $
p $-group actions on stable $\infty $-categories of chromatic height up to $ n $, extending a …

Let A→ B be a G-Galois extension of rings, or more generally of E∞-ring spectra in the
sense of Rognes. A basic question in algebraic K-theory asks how close the map K (A)→ K …

We introduce and study the notion of semiadditive height for higher semiadditive∞-
categories, which generalizes the chromatic height. We show that the higher semiadditive …

Higher semiadditive algebraic K-theory and redshift Page 1 Higher semiadditive algebraic K-theory
and redshift Shay Ben-Moshe and Tomer M. Schlank Compositio Math. 160 (2024), 237–287 …

We prove some $ K $-theoretic descent results for finite group actions on stable $\infty $-
categories, including the $ p $-group case of the Galois descent conjecture of Ausoni …

We construct Galois extensions of the T (n)-local sphere, lifting all finite abelian Galois
extensions of the K (n)-local sphere. This is achieved by realizing them as higher …

We prove a purity property in telescopically localized algebraic $ K $-theory of ring spectra:
For $ n\geq 1$, the $ T (n) $-localization of $ K (R) $ only depends on the $ T …

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 …

In this note we present a work in progresswhosemain purpose is to establish a categorified
version of sheaf theory. We present a notion of derived categorical sheaves, which is a …

We prove a higher chromatic analogue of Snaith's theorem which identifies the K–theory
spectrum as the localisation of the suspension spectrum of ℂ ℙ∞ away from the Bott class; …