We study prismatic crystals and their cohomology by using
q-Higgs modules (= a q-analogue of p-connections). When the base is
lying over the q-crystalline prism, they are locally described in
terms of q-Higgs modules and the associated complexes on...
iven an étale Zp-local system of rank n on an algebraic variety
X, continuous cohomology classes of the group GLn(Zp) give rise to
classes in (absolute) étale cohomology of the variety with
coefficients in Qp. These characteristic classes can be...
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...
What happens to an Lp function when one truncates its Fourier
transform to a domain? This question is now rather well understood,
thanks to famous results by Marcel Riesz and Charles Fefferman, and
the answer depends on the domain: if it is a...
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...