Topological cyclic homology is a refinement of Connes–Tsygan's cyclic homology which
was introduced by Bökstedt–Hsiang–Madsen in 1993 as an approximation to algebraic K …

To an Adams-type homology theory we associate the notion of a synthetic spectrum; this is a
product-preserving sheaf on the site of finite spectra with projective E-homology. We show …

We study the étale sheafification of algebraic K-theory, called étale K-theory. Our main
results show that étale K-theory is very close to a noncommutative invariant called Selmer K …

To a “stable homotopy theory”(a presentable, symmetric monoidal stable∞-category), we
naturally associate a category of finite étale algebra objects and, using Grothendieck's …

We define Grothendieck-Witt spectra in the setting of Poincaré-categories and show that
they fit into an extension with a K-and an L-theoretic part. As consequences, we deduce …

Redshift and multiplication for truncated Brown–Peterson spectra Page 1 Annals of
Mathematics 196 (2022), 1277–1351 https://doi.org/10.4007/annals.2022.196.3.6 Redshift and …

We develop a theory of cosupport and costratification in tensor triangular geometry. We
study the geometric relationship between support and cosupport, provide a conceptual …

Given a henselian pair $(R, I) $ of commutative rings, we show that the relative $ K $-theory
and relative topological cyclic homology with finite coefficients are identified via the …

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 …