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 …

The goal of this paper is to study the absolute prismatic cohomology of $ p $-adic formal
schemes. We do so by recasting the notion of a prismatic crystal on $\mathrm {Spf}(\mathbf …

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 establish a comparison isomorphism between prismatic cohomology and derived de
Rham cohomology respecting various structures, such as their Frobenius actions and …

These are notes for a course given at Princeton University in Fall 2022. The goal of this
course is to ultimately explain some work in progress of the author with Jacob Lurie on …

We prove several results showing that the algebraic $ K $-theory of valuation rings behaves
as though such rings were regular Noetherian, in particular an analogue of the Geisser …

The primary goal of this paper is to identify syntomic complexes with the p-adic étale Tate
twists of Geisser–Sato–Schneider on regular p-torsion-free schemes. Our methods apply …

We construct and study a $ t $-structure on $ p $-typical cyclotomic spectra and explain how
to recover crystalline cohomology of smooth schemes over perfect fields using this $ t …

We introduce the notion of a 𝑝-Cartier smooth algebra. It generalises that of a smooth
algebra and includes valuation rings over a perfectoid base. We give several …