Daniel Le

activity

20152025

most citedOn mod p local-global compatibility for GL_3 in the ordinary case

20 citations · 80 across the 18 of their papers we have counts for

collaborators

19 papers

math.NT2025

Serre weight conjectures for $GSp_{4}$

Daniel Le, Bao V. Le Hung, Heejong Lee

We prove the weight part of Serre's conjecture for Galois representations valued in $GSp_{4}$ that are tamely ramified with explicit genericity at places above $p$ as conjec…

math.NT2025

The weight part of Serre's conjecture over CM fields

Daniel Le, Bao V. Le Hung

Under some technical assumptions of a global nature, we establish the weight part of Serre's conjecture for mod $p$ Galois representations for CM fields that are tamely ramified an…

math.RT2024

Generic decompositions of Deligne--Lusztig representations

Daniel Le, Bao V. Le Hung, Brandon Levin +1

Let $G_{0}$ be a reductive group over $F_{p}$ with simply connected derived subgroup, (geometrically) connected center and Coxeter number $h + 1$ . We extend Jantzen's generic de…

math.NT2024

$K_{1}$ -invariants in the mod $p$ cohomology of $U (3)$ arithmetic manifolds

Daniel Le, Bao Viet Le Hung, Stefano Morra

Let $F / F^{+}$ be a CM extension and $H_{/ F^{+}}$ a definite unitary group in three variables that splits over $F$ . We describe Hecke isotypic components of mod $p$ algebraic modular fo…

math.NT2023

Colength one deformation rings

Daniel Le, Bao Le Hung, Stefano Morra +2

Let $K / Q_{p}$ be a finite unramified extension, $ρ : Gal (Q_{p} / K) \to GL_{n} (F_{p})$ a continuous representa…

math.NT2022

Extremal weights and a tameness criterion for mod $p$ Galois representations

Daniel Le, Bao Viet Le Hung, Brandon Levin +1

We study the weight part of Serre's conjecture for generic $n$ -dimensional mod $p$ Galois representations. We first generalize Herzig's conjecture to the case where the field is ra…

math.NT2022

Serre weights, Galois deformation rings, and local models

Daniel Le, Bao Viet Le Hung

We survey some recent progress on generalizations of conjectures of Serre concerning the cohomology of arithmetic groups, focusing primarily on the "weight" aspect. This is intimat…

math.NT2022★ 1 cited

Serre weights for three-dimensional wildly ramified Galois representations

Daniel Le, Bao Viet Le Hung, Brandon Levin +1

We formulate and prove the weight part of Serre's conjecture for three-dimensional mod $p$ Galois representations under a genericity condition when the field is unramified at $p$ .…

math.NT2021★ 2 cited

Moduli of Fontaine--Laffaille representations and a mod- $p$ local-global compatibility result

Daniel Le, Bao Viet Le Hung, Stefano Morra +2

Let $F / F^{+}$ be a CM field and let $v$ be a finite unramified place of $F$ above the prime $p$ . Let $\overline{r}: \mathrm{Gal}(\overline{\mathbb{Q}}/F)\rightarrow \math…

math.NT2020★ 1 cited

Local models for Galois deformation rings and applications

Daniel Le, Bao V. Le Hung, Brandon Levin +1

We construct projective varieties in mixed characteristic whose singularities model, in generic cases, those of tamely potentially crystalline Galois deformation rings for unramifi…

math.NT2019★ 16 cited

Diagrams in the mod $p$ cohomology of Shimura curves

Andrea Dotto, Daniel Le

We prove a local-global compatibility result in the mod $p$ Langlands program for $GL_{2} (Q_{p^{f}})$ . Namely, given a global residual representation $r ˉ$ that i…

math.RT2018★ 1 cited

On some nonadmissible smooth irreducible representations of $GL_{2}$

Daniel Le

Let $p > 2$ be a prime. We give examples of smooth absolutely irreducible representations of $GL_{2} (Q_{p^{3}})$ over $F_{p^{3}}$ which are not admissible.

math.NT2017★ 9 cited

Multiplicity one for wildly ramified representations

Daniel Le

Let $F$ be a totally real field in which $p$ is unramified. Let $r : G_{F} \to GL_{2} (F_{p})$ be a modular Galois representation which sati…

math.NT2016★ 13 cited

Weight elimination in Serre-type conjectures

Daniel Le, Bao V. Le Hung, Brandon Levin

We prove the weight elimination direction of the Serre weight conjectures as formulated by Herzig for forms of $U (n)$ which are compact at infinity and split at places dividing $p$ …

math.NT2016★ 11 cited

Multiplicity one at full congruence level

Daniel Le, Stefano Morra, Benjamin Schraen

Let $F$ be a totally real field in which $p$ is unramified. Let $r : G_{F} \to GL_{2} (F_{p})$ be a modular Galois representation which sati…

math.NT2016★ 3 cited

Serre weights and Breuil's lattice conjecture in dimension three

Daniel Le, Bao V. Le Hung, Brandon Levin +1

We prove in generic situations that the lattice in a tame type induced by the completed cohomology of a $U (3)$ -arithmetic manifold is purely local, i.e., only depends on the Galois…

math.NT2016★ 20 cited

On mod p local-global compatibility for GL_3 in the ordinary case

Florian Herzig, Daniel Le, Stefano Morra

Suppose that F/F+ is a CM extension of number fields in which the prime p splits completely and every other prime is unramified. Fix a place w|p of F. Suppose that rbar : Gal(F-bar…

math.NT2015★ 2 cited

Potentially crystalline deformation rings and Serre weight conjectures

Daniel Le, Bao V. Le Hung, Brandon Levin +1

We prove the weight part of Serre's conjecture in generic situations for forms of $U (3)$ which are compact at infinity and split at places dividing $p$ as conjectured by Herzig. We…

math.NT2015★ 1 cited

Lattices in the cohomology of $U (3)$ arithmetic manifolds

Daniel Le

Under hypotheses required for the Taylor-Wiles method, we prove for forms of $U (3)$ which are compact at infinity that the lattice structure on upper alcove algebraic vectors or on…

Serre weight conjectures for GSp4​

The weight part of Serre's conjecture over CM fields

Generic decompositions of Deligne--Lusztig representations

K1​-invariants in the mod p cohomology of U(3) arithmetic manifolds

Colength one deformation rings

Extremal weights and a tameness criterion for mod p Galois representations

Serre weights, Galois deformation rings, and local models

Serre weights for three-dimensional wildly ramified Galois representations

Moduli of Fontaine--Laffaille representations and a mod-p local-global compatibility result

Local models for Galois deformation rings and applications

Diagrams in the mod p cohomology of Shimura curves

On some nonadmissible smooth irreducible representations of GL2​

Multiplicity one for wildly ramified representations

Weight elimination in Serre-type conjectures

Multiplicity one at full congruence level

Serre weights and Breuil's lattice conjecture in dimension three

On mod p local-global compatibility for GL_3 in the ordinary case

Potentially crystalline deformation rings and Serre weight conjectures

Lattices in the cohomology of U(3) arithmetic manifolds

Serre weight conjectures for $GSp_{4}$

$K_{1}$ -invariants in the mod $p$ cohomology of $U (3)$ arithmetic manifolds

Extremal weights and a tameness criterion for mod $p$ Galois representations

Moduli of Fontaine--Laffaille representations and a mod- $p$ local-global compatibility result

Diagrams in the mod $p$ cohomology of Shimura curves

On some nonadmissible smooth irreducible representations of $GL_{2}$

Lattices in the cohomology of $U (3)$ arithmetic manifolds