On the modularity of elliptic curves over imaginary quadratic fields
A Caraiani, J Newton - arXiv preprint arXiv:2301.10509, 2023 - arxiv.org
In this paper, we establish the modularity of every elliptic curve $ E/F $, where $ F $ runs
over infinitely many imaginary quadratic fields, including $\mathbb {Q}(\sqrt {-d}) $ for $ d= 1 …
over infinitely many imaginary quadratic fields, including $\mathbb {Q}(\sqrt {-d}) $ for $ d= 1 …
Arthur's multiplicity formula for and restriction to
T Gee, O Taïbi - Journal de l'École polytechnique …, 2019 - jep.centre-mersenne.org
Arthur's multiplicity formula for GSp4 and restriction to Sp4 Page 1 Toby Gee & Olivier Taïbi
Arthur’s multiplicity formula for GSp4 and restriction to Sp4 Tome 6 (2019), p. 469-535. <http://jep.centre-mersenne.org/item/JEP_2019__6__469_0> …
Arthur’s multiplicity formula for GSp4 and restriction to Sp4 Tome 6 (2019), p. 469-535. <http://jep.centre-mersenne.org/item/JEP_2019__6__469_0> …
[PDF][PDF] Higher Hida and Coleman theories on the modular curve
G Boxer, V Pilloni - Épijournal de Géométrie Algébrique, 2022 - epiga.episciences.org
arXiv:2002.06845v2 [math.NT] 11 Sep 2022 Page 1 Épijournal de Géométrie Algébrique
epiga.episciences.org Volume 6 (2022), Article Nr. 16 Higher Hida and Coleman theories on the …
epiga.episciences.org Volume 6 (2022), Article Nr. 16 Higher Hida and Coleman theories on the …
[PDF][PDF] The explicit Local Langlands Correspondence for GSp4, Sp4 and stability (with an application to Modularity Lifting)
K Suzuki, Y Xu - arXiv preprint arXiv:2304.02622, 2023 - math.mit.edu
We give a purely local proof of the explicit Local Langlands Correspondence for GSp4 and
Sp4. Moreover, we give a unique characterization in terms of stability of L-packets and other …
Sp4. Moreover, we give a unique characterization in terms of stability of L-packets and other …
On the paramodularity of typical abelian surfaces
Generalizing the method of Faltings–Serre, we rigorously verify that certain abelian surfaces
without extra endomorphisms are paramodular. To compute the required Hecke …
without extra endomorphisms are paramodular. To compute the required Hecke …
Recent progress on Langlands reciprocity for : Shimura varieties and beyond
A Caraiani, SW Shin - arXiv preprint arXiv:2311.13382, 2023 - arxiv.org
The goal of these lecture notes is to survey progress on the global Langlands reciprocity
conjecture for $\mathrm {GL} _n $ over number fields from the last decade and a half. We …
conjecture for $\mathrm {GL} _n $ over number fields from the last decade and a half. We …
Reciprocity in the Langlands program since Fermat's Last Theorem
F Calegari - arXiv preprint arXiv:2109.14145, 2021 - arxiv.org
arXiv:2109.14145v1 [math.NT] 29 Sep 2021 Page 1 arXiv:2109.14145v1 [math.NT] 29 Sep
2021 RECIPROCITY IN THE LANGLANDS PROGRAM SINCE FERMAT’S LAST THEOREM …
2021 RECIPROCITY IN THE LANGLANDS PROGRAM SINCE FERMAT’S LAST THEOREM …
[PDF][PDF] Recent progress on Langlands reciprocity for GLn: Shimura varieties and beyond
A Caraiani, SW Shin - 2023 - math.berkeley.edu
The goal of these lecture notes is to survey progress on the global Langlands reciprocity
conjecture for GLn over number fields from the last decade and a half. We highlight results …
conjecture for GLn over number fields from the last decade and a half. We highlight results …
Local Intertwining Relations and Co-tempered -packets of Classical Groups
H Atobe, WT Gan, A Ichino, T Kaletha… - arXiv preprint arXiv …, 2024 - arxiv.org
The local intertwining relation is an identity that gives precise information about the action of
normalized intertwining operators on parabolically induced representations. We prove …
normalized intertwining operators on parabolically induced representations. We prove …
Mod local-global compatibility for in the ordinary case
J Enns, H Lee - Documenta Mathematica, 2024 - content.ems.press
Let F be a totally real field of even degree in which p splits completely. Let Nr WGf! GSp4.
xFp/be a modular Galois representation unramified at all finite places away from p and …
xFp/be a modular Galois representation unramified at all finite places away from p and …