3 papers
math.NT2026
A geometric Jacquet--Langlands correspondence for Shimura varieties
Pol van Hoften, Jack Sempliner
We formulate a conjecture predicting the existence of exotic isomorphisms between Igusa stacks associated to different Shimura data whose underlying groups are pure inner forms of…
math.NT2024
Cocycles for Kottwitz cohomology
Jack Sempliner, Richard Taylor
In his work on defining the pointed set B(G) for all local and global fields, Kottwitz introduced certain Galois gerbes and considered their 'algebraic' cohomology with values in a…
math.NT2024
On the Piatetski-Shapiro construction for integral models of Shimura varieties
Pol van Hoften, Jack Sempliner
We study the Piatetski-Shapiro construction, which takes a totally real field F and a Shimura datum (G,X) and produces a new Shimura datum (H,Y). If F is Galois, then the Galois gr…