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 …
Representations of p-adic groups over commutative rings
MF Vignéras - Prize LectureS, 2022 - ems.press
Motivated by the Langlands program in representation theory, number theory, and geometry,
the theory of representations of a reductive p-adic group, originally in complex vector …
the theory of representations of a reductive p-adic group, originally in complex vector …
Igusa stacks and the cohomology of Shimura varieties
We construct functorial Igusa stacks for all Hodge-type Shimura varieties, proving a
conjecture of Scholze and extending earlier results of the fourth-named author for PEL-type …
conjecture of Scholze and extending earlier results of the fourth-named author for PEL-type …
Modular functoriality in the local Langlands correspondence
T Feng - arXiv preprint arXiv:2312.12542, 2023 - arxiv.org
We develop a theory of Smith-Treumann localization and relative parity sheaves in the
context of Fargues-Scholze's Geometrization of the Local Langlands Correspondence. We …
context of Fargues-Scholze's Geometrization of the Local Langlands Correspondence. We …
Tate Cohomology of Whittaker Lattices and Base Change of Generic Representations of GLn
S Nadimpalli, S Dhar - International Mathematics Research …, 2024 - academic.oup.com
Let and be two distinct odd primes, and let be a positive integer. Let be a finite Galois
extension of degree of a-adic field. Let be the cardinality of the residue field of. Let be an …
extension of degree of a-adic field. Let be the cardinality of the residue field of. Let be an …
[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 …
Morphisms of character varieties
S Cotner - International Mathematics Research Notices, 2024 - academic.oup.com
Let be a field, let be (possibly disconnected) reductive groups over, and let be a finitely
generated group. Vinberg and Martin have shown that the induced morphism is finite. In this …
generated group. Vinberg and Martin have shown that the induced morphism is finite. In this …
Second adjointness and cuspidal supports at the categorical level
Y Takaya - arXiv preprint arXiv:2408.04582, 2024 - arxiv.org
We prove the second adjointness in the setting of the categorical local Langlands
correspondence. Moreover, we study the relation between Eisenstein series and cuspidal …
correspondence. Moreover, we study the relation between Eisenstein series and cuspidal …
Families of canonical local periods on spherical varieties
L Cai, Y Fan - Mathematische Annalen, 2024 - Springer
We consider the variation of canonical local periods on spherical varieties proposed by
Sakellaridis–Venkatesh in families. We formulate conjectures for the rationality and …
Sakellaridis–Venkatesh in families. We formulate conjectures for the rationality and …
Local Langlands in families: The banal case
JF Dat, D Helm, R Kurinczuk, G Moss - arXiv preprint arXiv:2406.09283, 2024 - arxiv.org
We state a conjecture, local Langlands in families, connecting the centre of the category of
smooth representations on $\mathbb {Z}[\sqrt {q}^{-1}] $-modules of a quasi-split $ p $-adic …
smooth representations on $\mathbb {Z}[\sqrt {q}^{-1}] $-modules of a quasi-split $ p $-adic …