2 citations · 4 across the 9 of their papers we have counts for
11 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…
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…
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…
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…
On the connectedness of -adic period domains
Ian Gleason, João Lourenço
We prove that all -adic period domains (and their non-minuscule analogues) are geometrically connected. This answers a question of Hartl [Har13] and has interesting consequences…
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…
Tubular neighborhoods of local models
Ian Gleason, João Lourenço
We show that the v-sheaf local models of moduli spaces of -adic shtukas are unibranch. In particular, this proves that the scheme-theoretic local models defined in our joint wor…
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…
On the geometric connected components of moduli spaces of p-adic shtukas and local Shimura varieties
Ian Gleason
We study topological properties of moduli spaces of p-adic shtukas and local Shimura varieties. On one hand, we construct and study the specialization map for moduli spaces of p-ad…
Specialization maps for Scholze's category of diamonds
Ian Gleason
We introduce the specialization map in Scholzes theory of diamonds. We consider v-sheaves that behave like formal schemes and call them kimberlites. We attach to them: a reduced sp…
Products of abstract polytopes
Ian Gleason, Isabel Hubard
Given two convex polytopes, the join, the cartesian product and the direct sum of them are well understood. In this paper we extend these three kinds of products to abstract polyto…