The main result of this paper is the existence of Galois representations associated with the
mod p (or mod pm) cohomology of the locally symmetric spaces for GLn over a totally real or …

We introduce various affine Grassmannians, study their geometric properties, and give some
applications. We also discuss the geometric Satake equivalence. These are the expanded …

The goal of this paper is to show that the cohomology of compact unitary Shimura varieties is
concentrated in the middle degree and torsion-free, after localizing at a maximal ideal of the …

We propose a duality in the relative Langlands program. This duality pairs a Hamiltonian
space for a group $ G $ with a Hamiltonian space under its dual group $\check {G} $, and …

For any reductive group $ G $ over a global function field, we use the cohomology of $ G $-
shtukas with multiple modifications and the geometric Satake equivalence to prove the …

We extend our methods from Scholze (Invent. Math. 2012, doi: 10.1007/s00222-012-0419-y)
to reprove the Local Langlands Correspondence for GL n over p-adic fields as well as the …

THE ASYMPTOTIC GROWTH OF TORSION HOMOLOGY FOR ARITHMETIC GROUPS Page
1 J. Inst. Math. Jussieu (2013) 12(2), 391–447 391 doi:10.1017/S1474748012000667 c …

We formulate a few conjectures on some hypothetical coherent sheaves on the stacks of
arithmetic local Langlands parameters, including their roles played in the local-global …

arXiv:2210.01404v2 [math.NT] 1 Feb 2023 Page 1 An introduction to the categorical p-adic
Langlands program Matthew Emerton, Toby Gee, and Eugen Hellmann Abstract. We give an …

We show that abelian surfaces (and consequently curves of genus 2) over totally real fields
are potentially modular. As a consequence, we obtain the expected meromorphic …