105 citations · 417 across the 30 of their papers we have counts for
39 papers
Sheared Witt Vectors
Bhargav Bhatt, Akhil Mathew, Vadim Vologodsky
V. Drinfeld and E. Lau introduced a ``decompletion'' of the ring of -typical Witt vectors, following earlier work of T. Zink. The goal of this paper is to offer an exposition of…
The mod Riemann-Hilbert correspondence and the perfect site
Akhil Mathew
The mod Riemann-Hilbert correspondence (in covariant and contravariant forms) relates -étale sheaves on the spectrum of an -algebra and Frobeniu…
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…
Syntomic complexes and -adic étale Tate twists
Bhargav Bhatt, Akhil Mathew
The primary goal of this paper is to identify syntomic complexes with the -adic étale Tate twists of Geisser--Schneider--Sato on regular -torsionfree schemes. Our methods app…
K-theory and polynomial functors
Clark Barwick, Saul Glasman, Akhil Mathew +1
We show that the algebraic K-theory space of stable infinity-categories is canonically functorial in polynomial functors. As a consequence, we obtain a new proof of Bökstedt's calc…
Some recent advances in topological Hochschild homology
Akhil Mathew
We give an account of the construction of the Bhatt--Morrow--Scholze motivic filtration on topological cyclic homology and related invariants, focusing on the case of equal charact…
Descent and vanishing in chromatic algebraic -theory via group actions
Dustin Clausen, Akhil Mathew, Niko Naumann +1
We prove some -theoretic descent results for finite group actions on stable -categories, including the -group case of the Galois descent conjecture of Ausoni-Rognes.…
On -local
Akhil Mathew
We discuss some general properties of and its -localization. We prove that after -localization, of -algebras is a truncating in…
On the Beilinson fiber square
Benjamin Antieau, Akhil Mathew, Matthew Morrow +1
Using topological cyclic homology, we give a refinement of Beilinson's -adic Goodwillie isomorphism between relative continuous -theory and cyclic homology. As a result, we g…
Remarks on -local -theory
Bhargav Bhatt, Dustin Clausen, Akhil Mathew
We prove two basic structural properties of the algebraic -theory of rings after -localization at an implicit prime . Our first result (also recently obtained by Land--…
Purity in chromatically localized algebraic -theory
Markus Land, Akhil Mathew, Lennart Meier +1
We prove a purity property in telescopically localized algebraic -theory of ring spectra: For , the -localization of only depends on the $T(0)\oplus \dots…
Faithfully flat descent of almost perfect complexes in rigid geometry
Akhil Mathew
We prove a version of faithfully flat descent in rigid analytic geometry, for almost perfect complexes and without finiteness assumptions on the rings involved. This extends result…
Counterexamples to Hochschild--Kostant--Rosenberg in characteristic
Benjamin Antieau, Bhargav Bhatt, Akhil Mathew
We give counterexamples to the degeneration of the HKR spectral sequence in characteristic , both in the untwisted and twisted settings. We also prove that the de Rham--$\mathrm…
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…
Deformation Theory and Partition Lie Algebras
Lukas Brantner, Akhil Mathew
A theorem of Lurie and Pridham establishes a correspondence between formal moduli problems and differential graded Lie algebras in characteristic zero, thereby formalising a well-k…
The arc-topology
Bhargav Bhatt, Akhil Mathew
We study a Grothendieck topology on schemes which we call the -topology. This topology is a refinement of the -topology (the pro-version of Voevodsky's -topolog…
Revisiting the de Rham-Witt complex
Bhargav Bhatt, Jacob Lurie, Akhil Mathew
The goal of this paper is to offer a new construction of the de Rham-Witt complex of smooth varieties over perfect fields of characteristic . We introduce a category of cochai…
K-theory and topological cyclic homology of henselian pairs
Dustin Clausen, Akhil Mathew, Matthew Morrow
Given a henselian pair of commutative rings, we show that the relative -theory and relative topological cyclic homology with finite coefficients are identified via the…
Kaledin's degeneration theorem and topological Hochschild homology
Akhil Mathew
We give a short proof of Kaledin's theorem on the degeneration of the noncommutative Hodge-to-de Rham spectral sequence. Our approach is based on topological Hochschild homology an…
On the Blumberg-Mandell Künneth theorem for TP
Benjamin Antieau, Akhil Mathew, Thomas Nikolaus
We give a new proof of the recent Künneth theorem for periodic topological cyclic homology (TP) of smooth and proper dg categories over perfect fields of characteristic p>0 due to…
Monadicity of the Bousfield-Kuhn functor
Rosona Eldred, Gijs Heuts, Akhil Mathew +1
We consider the localization of the -category of spaces at the -periodic equivalences, the case being rational homotopy theory. We prove that this localization i…
Examples of descent up to nilpotence
Akhil Mathew
We give a survey of the ideas of descent and nilpotence. We focus on examples arising from chromatic homotopy theory and from group actions, as well as a few examples in algebra.
A short proof of telescopic Tate vanishing
Dustin Clausen, Akhil Mathew
We give a short proof of a theorem of Kuhn that Tate constructions for finite group actions vanish in telescopically localized stable homotopy theory. In particular, we observe tha…
Descent in algebraic -theory and a conjecture of Ausoni-Rognes
Dustin Clausen, Akhil Mathew, Niko Naumann +1
Let be a -Galois extension of rings, or more generally of -ring spectra in the sense of Rognes. A basic question in algebraic -theory asks how cl…