We introduce the notion of a prism, which may be regarded as a" deperfection" of the notion
of a perfectoid ring. Using prisms, we attach a ringed site---the prismatic site---to a p-adic …

In mixed characteristic and in equal characteristic pp we define a filtration on topological
Hochschild homology and its variants. This filtration is an analogue of the filtration of …

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 …

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 …

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 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 …

We define, for each quasisyntomic ring R (in the sense of Bhatt et al., Publ. Math. IHES 129
(2019), 199–310), a category of admissible prismatic Dieudonné crystals over R and a …

At each prime $ p $ and height $ n+ 1\ge 2$, we prove that the telescopic and chromatic
localizations of spectra differ. Specifically, for $\mathbb {Z} $ acting by Adams operations on …

We construct a theory of motivic cohomology for quasi-compact, quasi-separated schemes
of equal characteristic, which is related to non-connective algebraic $ K $-theory via an …

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 …