Geometrization of the local Langlands correspondence
L Fargues, P Scholze - arXiv preprint arXiv:2102.13459, 2021 - arxiv.org
Following the idea of [Far16], we develop the foundations of the geometric Langlands
program on the Fargues--Fontaine curve. In particular, we define a category of $\ell $-adic …
program on the Fargues--Fontaine curve. In particular, we define a category of $\ell $-adic …
Coherent sheaves on the stack of Langlands parameters
X Zhu - arXiv preprint arXiv:2008.02998, 2020 - arxiv.org
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 …
arithmetic local Langlands parameters, including their roles played in the local-global …
Finiteness for Hecke algebras of 𝑝-adic groups
Let $ G $ be a reductive group over a non-archimedean local field $ F $ of residue
characteristic $ p $. We prove that the Hecke algebras of $ G (F) $, with coefficients in any …
characteristic $ p $. We prove that the Hecke algebras of $ G (F) $, with coefficients in any …
Torsion vanishing for some Shimura varieties
L Hamann, SY Lee - arXiv preprint arXiv:2309.08705, 2023 - arxiv.org
We generalize the torsion vanishing results of Caraiani-Scholze and Koshikawa. Our results
apply to the cohomology of general Shimura varieties $(\mathbf {G}, X) $ of PEL type $ A …
apply to the cohomology of general Shimura varieties $(\mathbf {G}, X) $ of PEL type $ A …
Coherent Springer theory and the categorical Deligne-Langlands correspondence
Kazhdan and Lusztig identified the affine Hecke algebra ℋ with an equivariant K-group of
the Steinberg variety, and applied this to prove the Deligne-Langlands conjecture, ie, the …
the Steinberg variety, and applied this to prove the Deligne-Langlands conjecture, ie, the …
Meromorphic vector bundles on the Fargues--Fontaine curve
I Gleason, AB Ivanov - arXiv preprint arXiv:2307.00887, 2023 - arxiv.org
We introduce and study the stack of\textit {meromorphic} $ G $-bundles on the Fargues--
Fontaine curve. This object defines a correspondence between the Kottwitz stack $\mathfrak …
Fontaine curve. This object defines a correspondence between the Kottwitz stack $\mathfrak …
Compatibility of the Fargues--Scholze correspondence for unitary groups
AB Meli, L Hamann, KH Nguyen - arXiv preprint arXiv:2207.13193, 2022 - arxiv.org
We study unramified unitary and unitary similitude groups in an odd number of variables.
Using work of the first and third named authors on the Kottwitz Conjecture for the similitude …
Using work of the first and third named authors on the Kottwitz Conjecture for the similitude …
Local Langlands correspondences
M Harris - arXiv preprint arXiv:2205.03848, 2022 - arxiv.org
The first part of this article is a review of the properties expected of any local Langlands
correspondence that aims to be considered" canonical," and of known results that establish …
correspondence that aims to be considered" canonical," and of known results that establish …
On the derived category of the Iwahori–Hecke algebra
E Hellmann - Compositio Mathematica, 2023 - cambridge.org
We state a conjecture that relates the derived category of smooth representations of a by
showing that the functor should be given by the derived tensor product with the family of …
showing that the functor should be given by the derived tensor product with the family of …
The geometric Breuil–Mézard conjecture for two-dimensional potentially Barsotti–Tate Galois representations
Caraiani was supported in part by NSF grant DMS-1501064, by a Royal Society University
Research Fellowship, and by ERC Starting Grant 804176. Emerton was supported in part by …
Research Fellowship, and by ERC Starting Grant 804176. Emerton was supported in part by …