8 papers
On -local
Akhil Mathew
We discuss some general properties of and its -localization. We prove that after -localization, of -algebras is a truncating in…
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--…
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…
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…