In recent work with Antieau and Nikolaus we use prismatic
cohomology to compute algebraic K-theory of Z/pn and similar
rings. Our approach is based on a new description of absolute
prismatic cohomology, which can be made completely algorithmic
in...
Recently the work of Fargues--Scholze provides a geometrization
of the local Langlands conjecture. It is natural to ask if in this
context any form of local-global compatibility can be
stated/verified. We discuss some expectations and evidences...
The p-adic Simpson correspondence aims to give a non-abelian
generalisation of the Hodge-Tate decomposition. Following an idea
of Faltings, it should relate pro-étale vector bundles on smooth
rigid spaces over Cp to Higgs bundles. In this talk, I...
Multiplier ideals and test ideals are ways to measure
singularities in characteristic zero and p > 0 respectively.
In characteristic zero, multiplier ideals are computed by a
sufficiently large blowup by comparing the canonical module of the
base...
Since the original conjectures of Beilinson and Lichtenbaum in
the 80s, several versions of motivic cohomology have been
introduced and developed, notably by Voevodsky. Most classically,
Bloch's higher Chow groups provide the accepted theory of...