The geometric Breuil-M\'ezard conjecture for two-dimensional potentially Barsotti-Tate Galois representations
arXiv:2207.05235v1 [math.NT] 12 Jul 2022 Page 1 arXiv:2207.05235v1 [math.NT] 12 Jul 2022
THE GEOMETRIC BREUIL–MÉZARD CONJECTURE FOR TWO-DIMENSIONAL …
THE GEOMETRIC BREUIL–MÉZARD CONJECTURE FOR TWO-DIMENSIONAL …
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 …
[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 …
[PDF][PDF] Complex matrix inversion via real matrix inversions
We study the inversion analog of the well-known Gauss algorithm for multiplying complex
matrices. A simple version is (A+ iB)− 1=(A+ BA− 1B)− 1− iA− 1B (A+ BA− 1B)− 1 when A is …
matrices. A simple version is (A+ iB)− 1=(A+ BA− 1B)− 1− iA− 1B (A+ BA− 1B)− 1 when A is …
On the effective version of Serre's open image theorem
J Mayle, T Wang - Bulletin of the London Mathematical Society, 2024 - Wiley Online Library
Abstract Let E/QE/Q be an elliptic curve without complex multiplication. By Serre's open
image theorem, the mod ℓ ℓ Galois representation ρ¯ E, ℓ ρ_E,ℓ of EE is surjective for each …
image theorem, the mod ℓ ℓ Galois representation ρ¯ E, ℓ ρ_E,ℓ of EE is surjective for each …
Power values of power sums: a survey
Research on power values of power sums has gained much attention of late, partially due to
the explosion of refinements in multiple advanced tools in (computational) number theory in …
the explosion of refinements in multiple advanced tools in (computational) number theory in …
Modularity of special motives of rank four associated with Calabi-Yau threefolds
K Bönisch - 2023 - bonndoc.ulb.uni-bonn.de
In this thesis, we study modularity properties of pure motives and mixed period matrices of
rank four. The pure motives that we consider are associated with Calabi-Yau threefolds …
rank four. The pure motives that we consider are associated with Calabi-Yau threefolds …
Motivic action for Siegel modular forms
A Horawa, K Prasanna - arXiv preprint arXiv:2307.04115, 2023 - arxiv.org
We study the coherent cohomology of automorphic sheaves corresponding to Siegel
modular forms $ f $ of low weight on ${\rm GSp}(4) $ Shimura varieties. Inspired by the work …
modular forms $ f $ of low weight on ${\rm GSp}(4) $ Shimura varieties. Inspired by the work …
Vign\'eras orbifolds: isospectrality, regulators, and torsion homology
A Bartel, A Page - arXiv preprint arXiv:2407.07240, 2024 - arxiv.org
We develop a new approach to the isospectrality of the orbifolds constructed by Vign\'eras.
We give fine sufficient criteria for i-isospectrality in given degree i and for representation …
We give fine sufficient criteria for i-isospectrality in given degree i and for representation …
Prolongement analytique de fonctions et de fonctions
P Colmez - arXiv preprint arXiv:2311.15905, 2023 - arxiv.org
Wiles' work on Fermat's last Theorem highlighted the power of $ p $-adic methods to prove
the existence of analytic continuations of $\zeta $ and $ L $ functions. These methods have …
the existence of analytic continuations of $\zeta $ and $ L $ functions. These methods have …