9 papers
On the Schematic and Analytic Constructions of the Local Langlands Category
Ian Gleason, Linus Hamann, Alexander B. Ivanov +2
We prove a folklore conjecture identifying two categorical enhancements of the automorphic side of the local Langlands correspondence. Concretely, we construct an equivalence for t…
Meromorphic vector bundles on the Fargues--Fontaine curve
Ian Gleason, Alexander B. Ivanov, Felix Zillinger
We introduce and study the stack of \textit{meromorphic} -bundles on the Fargues--Fontaine curve. This object defines a correspondence between the Kottwitz stack $\mathfrak{B}(G…
On the -adic theory of local models
Johannes Anschütz, Ian Gleason, João Lourenço +1
We prove the Scholze--Weinstein conjecture on the existence and uniqueness of local models for local Shimura varieties, as well as the test function conjecture of Haines--Kottwitz…
Stacks of p-adic shtukas and spatial kimberlites
Ian Gleason
The main purpose of this article is to show that the special Newton polygon map from the stack of p-adic shtukas to the stack of G-bundles on the Fargues--Fontaine curve is represe…
The connected components of affine Deligne--Lusztig varieties
Ian Gleason, Dong Gyu Lim, Yujie Xu
We compute the connected components of arbitrary parahoric level affine Deligne-Lusztig varieties and local Shimura varieties, thus resolving a folklore conjecture in full generali…
Perfectoid Nullstellensatz: Results and counterexamples
Ian Gleason
We give necessary conditions and we give sufficient conditions for perfectoid Nullstellensatz to hold. As a consequence, we prove that perfectoid Nullstellensatz does not hold for…