A. Mathew

activity

20172022

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5 papers · 1 filter

math.KT2022

The K-theory of perfectoid rings

Benjamin Antieau, Akhil Mathew, Matthew Morrow

We establish various properties of the p-adic algebraic K-theory of smooth algebras over perfectoid rings living over perfectoid valuation rings. In particular, the p-adic K-theory…

math.KT2020

On $K (1)$ -local $TR$

Akhil Mathew

We discuss some general properties of $TR$ and its $K (1)$ -localization. We prove that after $K (1)$ -localization, $TR$ of $H Z$ -algebras is a truncating in…

math.KT2020

Remarks on $K (1)$ -local $K$ -theory

Bhargav Bhatt, Dustin Clausen, Akhil Mathew

We prove two basic structural properties of the algebraic $K$ -theory of rings after $K (1)$ -localization at an implicit prime $p$ . Our first result (also recently obtained by Land--…

math.KT2019

Hyperdescent and étale K-theory

Dustin Clausen, Akhil Mathew

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…

math.KT2018

K-theory and topological cyclic homology of henselian pairs

Dustin Clausen, Akhil Mathew, Matthew Morrow

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…

The K-theory of perfectoid rings

On K(1)-local TR

Remarks on K(1)-local K-theory

Hyperdescent and étale K-theory

K-theory and topological cyclic homology of henselian pairs

On $K (1)$ -local $TR$

Remarks on $K (1)$ -local $K$ -theory