Special Year 2023-24: p-adic Arithmetic Geometry

Abstract: 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...

Abstract: 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...

Abstract: 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...

Abstract: 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...

Abstract: 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...

Sponsored by Dr. John P. Hempel and Simons Foundation

Organizers: Bhargav Bhatt (IAS/Princeton/Michigan), Johan DeJong (Columbia/IAS), Jacob Lurie (IAS)

Invited Speakers:
Kestutis Cesnavicius, Université Paris-Saclay/IAS
Pierre Colmez, IMJ-PRG/IAS
Lars...

A smooth, oriented n-manifold is called a homotopy sphere if it is homeomorphic, but not necessarily diffeomorphic, to the standard n-sphere. In dimensions $n>4$, one often studies the group Θn of homotopy spheres up to orientation-preserving...

In chromatic homotopy theory, an object like the sphere spectrum $S^0$ is studied by means of its "localizations", much as an abelian group can be localized at each prime p.  Remarkably, the "primes" $K(n)$ in the homotopy setting correspond to...

In joint work in progress with Anschütz and Le Bras we aim to construct a 6-functor formalism for quasicoherent sheaves on the relative Fargues-Fontaine curve over rigid-analytic varieties (and even general v-stacks), providing new insights into the...

The recent work of Drinfeld and Bhatt-Lurie led to a new geometric approach to p-adic cohomology theories, analogously to what was done earlier in Hodge theory by Simpson. This stacky perspective gives in particular a new approach to p-adic non...