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 …

Some recent advances in topological Hochschild homology - Mathew - 2022 - Bulletin of the
London Mathematical Society - Wiley Online Library Skip to Article Content Skip to Article …

Equivariant homotopy theory started from geometrically motivated questions about
symmetries of manifolds. Several important equivariant phenomena occur not just for a …

We give an overview of the applications of noncommutative geometry to physics. Our focus
is entirely on the conceptual ideas, rather than on the underlying technicalities. Starting …

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 …

Using topological cyclic homology, we give a refinement of Beilinson'sp-adic Goodwillie
isomorphism between relative continuous K-theory and cyclic homology. As a result, we …

To any pullback square of ring spectra we associate a new ring spectrum and use it to
describe the failure of excision in algebraic K-theory. The construction of this new ring …

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 show that Lubin--Tate theories attached to algebraically closed fields are characterized
among $ T (n) $-local $\mathbb {E} _ {\infty} $-rings as those that satisfy an analogue of …

Topological cyclic homology is a manifestation of Waldhausen's vision that the cyclic theory
of Connes and Tsygan should be developed with the initial ring S of higher algebra as base …