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math.AG2019
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…
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…