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 …
On the structure of some p-adic period domains
M Chen, L Fargues, X Shen - arXiv preprint arXiv:1710.06935, 2017 - arxiv.org
We prove the Fargues-Rapoport conjecture for p-adic period domains: for a reductive group
G over a p-adic field and a minuscule cocharacter {\mu} of G, the weakly admissible locus …
G over a p-adic field and a minuscule cocharacter {\mu} of G, the weakly admissible locus …
On the étale cohomology of Hilbert modular varieties with torsion coefficients
A Caraiani, M Tamiozzo - Compositio Mathematica, 2023 - cambridge.org
We study the étale cohomology of Hilbert modular varieties, building on the methods
introduced by Caraiani and Scholze for unitary Shimura varieties. We obtain the analogous …
introduced by Caraiani and Scholze for unitary Shimura varieties. We obtain the analogous …
[PDF][PDF] On the geometrization of the local Langlands correspondence
N Imai - arXiv preprint arXiv:2408.16571, 2024 - arxiv.org
arXiv:2408.16571v1 [math.NT] 29 Aug 2024 Page 1 arXiv:2408.16571v1 [math.NT] 29 Aug 2024
ON THE GEOMETRIZATION OF THE LOCAL LANGLANDS CORRESPONDENCE NAOKI IMAI …
ON THE GEOMETRIZATION OF THE LOCAL LANGLANDS CORRESPONDENCE NAOKI IMAI …
Dualizing complexes on the moduli of parabolic bundles
L Hamann, N Imai - arXiv preprint arXiv:2401.06342, 2024 - arxiv.org
For a non-archimedean local field $ F $ and a connected reductive group $ G $ over $ F $
equipped with a parabolic subgroup $ P $, we show that the dualizing complex on $\mathrm …
equipped with a parabolic subgroup $ P $, we show that the dualizing complex on $\mathrm …
Moduli of local shtukas and Harris's conjecture
D Hansen - Tunisian Journal of Mathematics, 2021 - msp.org
We prove, under a certain assumption of “Hodge–Newton reducibility”, a strong form of a
conjecture of Harris on the cohomology of moduli spaces of mixed-characteristic local …
conjecture of Harris on the cohomology of moduli spaces of mixed-characteristic local …
Convolution morphisms and Kottwitz conjecture
N Imai - arXiv preprint arXiv:1909.02328, 2019 - arxiv.org
We define etale cohomology of the moduli spaces of mixed characteristic local shtukas so
that it gives smooth representations including the case where the relevant elements of the …
that it gives smooth representations including the case where the relevant elements of the …
Hodge–Newton filtration for -divisible groups with ramified endomorphism structure
A Marrama - Documenta Mathematica, 2022 - content.ems.press
Let OK be a complete discrete valuation ring of mixed characteristic (0, p) with perfect
residue field. We prove the existence of the Hodge-Newton filtration for p-divisible groups …
residue field. We prove the existence of the Hodge-Newton filtration for p-divisible groups …
Geometrization of Local Langlands and the Cohomology of Shimura Varieties
L Hamann - 2023 - search.proquest.com
Fargues and Scholze showed that a candidate for the local Langlands correspondence for p-
adic reductive groups G/ℚ p could be realized in terms of a geometric Langlands …
adic reductive groups G/ℚ p could be realized in terms of a geometric Langlands …
Zelevinsky Duality on Basic Local Shimura Varieties
L Hamann - arXiv preprint arXiv:2109.01213, 2021 - arxiv.org
We give a simple proof of a general result describing the action of the Zelevinsky involution
on the cohomology of certain basic local Shimura varieties, using the machinery of Fargues …
on the cohomology of certain basic local Shimura varieties, using the machinery of Fargues …