F. Herzig

activity

20082026

most citedThe weight in a Serre-type conjecture for tame n-dimensional Galois representations

109 citations · 454 across the 24 of their papers we have counts for

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22 papers · 1 filter

math.NT2026

To be or not to be local

Christophe Breuil, Florian Herzig, Yongquan Hu +4

Let $p$ be a prime number and $K$ a finite unramified extension of $Q_{p}$ . For a smooth representation $π$ of $GL_{2} (K)$ occurring in some Hecke eigenspace of the m…

math.NT2025

On the constituents of the mod $p$ cohomology of Shimura curves

Christophe Breuil, Florian Herzig, Yongquan Hu +2

Let $p$ be a prime number and $K$ a finite unramified extension of $Q_{p}$ . When $p$ is large enough with respect to $[K : Q_{p}]$ and under mild genericity assumptions…

math.NT2025

Finite length for unramified $GL_{2}$

Christophe Breuil, Florian Herzig, Yongquan Hu +2

Let $p$ be a prime number and $K$ a finite unramified extension of $Q_{p}$ . If $p$ is large enough with respect to $[K : Q_{p}]$ and under mild genericity assumptions,…

math.NT2023★ 2 cited

On the irreducibility of $p$ -adic Banach principal series of $p$ -adic $GL_{3}$

Noriyuki Abe, Florian Herzig

We establish an optimal (topological) irreducibility criterion for $p$ -adic Banach principal series of $GL_{n} (F)$ , where $F / Q_{p}$ is finite and $n \leq 3$ . This is…

math.NT2023★ 2 cited

On the irreducibility of $p$ -adic Banach principal series of $p$ -adic reductive groups

Noriyuki Abe, Florian Herzig

Suppose that $G$ is the group of $F$ -points of a connected reductive group over $F$ , where $F / Q_{p}$ is a finite extension. We study the (topological) irreducibility of prin…

math.NT2022

Multivariable ( $φ$ , $O_{K}^{\times}$ )-modules and local-global compatibility

Christophe Breuil, Florian Herzig, Yongquan Hu +2

Let $p$ be a prime number, $K$ a finite unramified extension of $Q_{p}$ and $F$ a finite extension of $F_{p}$ . Using perfectoid spaces we associate to any fi…

math.NT2021★ 5 cited

Conjectures and results on modular representations of $GL_{n} (K)$ for a $p$ -adic field $K$

Christophe Breuil, Florian Herzig, Yongquan Hu +2

Let $p$ be a prime number and $K$ a finite extension of $Q_{p}$ . We state conjectures on the smooth representations of $GL_{n} (K)$ that occur in spaces of mod $p$ aut…

math.NT2020★ 1 cited

Gelfand-Kirillov dimension and mod p cohomology for GL2

Christophe Breuil, Florian Herzig, Yongquan Hu +2

Let $p$ be a prime number, $F$ a totally real number field unramified at places above $p$ and $D$ a quaternion algebra of center $F$ split at places above $p$ and at no more than o…

math.NT2018★ 3 cited

Towards the finite slope part for $GL_{n}$

Christophe Breuil, Florian Herzig

Let $L$ be a finite extension of $Q_{p}$ and $n \geq 2$ . We associate to a crystabelline $n$ -dimensional representation of $Gal (L / L)$ satisfying mild gener…

math.NT2018★ 1 cited

Inverse Satake isomorphism and change of weight

Noriyuki Abe, Florian Herzig, Marie-France Vignéras

Let $G$ be any connected reductive $p$ -adic group. Let $K \subset G$ be any special parahoric subgroup and $V, V^{'}$ be any two irreducible smooth $F_{p} [K]$ -modules.…

math.NT2017★ 6 cited

Questions on mod p representations of reductive p-adic groups

Noriyuki Abe, Guy Henniart, Florian Herzig +1

This is a list of questions raised by our joint work arXiv:1412.0737 and its sequels.

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

General Serre weight conjectures

Toby Gee, Florian Herzig, David Savitt

We formulate a number of related generalisations of the weight part of Serre's conjecture to the case of GL(n) over an arbitrary number field, motivated by the formalism of the Bre…

math.NT2015

Potentially crystalline lifts of certain prescribed types

Toby Gee, Florian Herzig, Tong Liu +1

We prove several results concerning the existence of potentially crystalline lifts with prescribed Hodge-Tate weights and inertial types of a given n-dimensional mod p representati…

math.NT2014★ 33 cited

A classification of irreducible admissible mod p representations of p-adic reductive groups

Noriyuki Abe, Guy Henniart, Florian Herzig +1

Let F be a locally compact non-archimedean field, p its residue characteristic, and G a connected reductive group over F. Let C an algebraically closed field of characteristic p. W…

math.NT2012★ 23 cited

Ordinary representations of G(Q_p) and fundamental algebraic representations

Christophe Breuil, Florian Herzig

Let G be a split connected reductive algebraic group over Q_p such that both G and its dual group G-hat have connected centres. Motivated by a hypothetical p-adic Langlands corresp…

math.NT2011★ 71 cited

Adequate subgroups

Robert Guralnick, Florian Herzig, Richard Taylor +1

We study adequate subgroups of $G L_{n}$ over a finite field. This notion is useful in the study of automorphy lifting theorems. In particular, we give a sufficient condition for a su…

math.NT2011★ 27 cited

Weight cycling and Serre-type conjectures for unitary groups

Matthew Emerton, Toby Gee, Florian Herzig

We prove that for forms of U(3) which are compact at infinity and split at places dividing a prime p, in generic situations the Serre weights of a mod p modular Galois representati…

math.NT2010★ 72 cited

The classification of irreducible admissible mod p representations of a p-adic GL_n

Florian Herzig

Let F be a finite extension of Q_p. Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive gro…

math.NT2009★ 61 cited

A Satake isomorphism in characteristic p

Florian Herzig

Suppose that G is a connected reductive group over a p-adic field F, that K is a hyperspecial maximal compact subgroup of G(F), and that V is an irreducible representation of K ove…

math.NT2008★ 7 cited

Conjecture de type de Serre et formes compagnons pour GSp_4

Florian Herzig, Jacques Tilouine

We present a Serre-type conjecture on the modularity of four-dimensional symplectic mod p Galois representations. We assume that the Galois representation is irreducible and odd (i…

math.NT2008★ 109 cited

The weight in a Serre-type conjecture for tame n-dimensional Galois representations

Florian Herzig

We formulate a Serre-type conjecture for n-dimensional Galois representations that are tamely ramified at p. The weights are predicted using a representation-theoretic recipe. For…

To be or not to be local

On the constituents of the mod p cohomology of Shimura curves

Finite length for unramified GL2​

On the irreducibility of p-adic Banach principal series of p-adic GL3​

On the irreducibility of p-adic Banach principal series of p-adic reductive groups

Multivariable (φ,OK×​)-modules and local-global compatibility

Conjectures and results on modular representations of GLn​(K) for a p-adic field K

Gelfand-Kirillov dimension and mod p cohomology for GL2

Towards the finite slope part for GLn​

Inverse Satake isomorphism and change of weight

Questions on mod p representations of reductive p-adic groups

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

General Serre weight conjectures

Potentially crystalline lifts of certain prescribed types

A classification of irreducible admissible mod p representations of p-adic reductive groups

Ordinary representations of G(Q_p) and fundamental algebraic representations

Adequate subgroups

Weight cycling and Serre-type conjectures for unitary groups

The classification of irreducible admissible mod p representations of a p-adic GL_n

A Satake isomorphism in characteristic p

Conjecture de type de Serre et formes compagnons pour GSp_4

The weight in a Serre-type conjecture for tame n-dimensional Galois representations

On the constituents of the mod $p$ cohomology of Shimura curves

Finite length for unramified $GL_{2}$

On the irreducibility of $p$ -adic Banach principal series of $p$ -adic $GL_{3}$

On the irreducibility of $p$ -adic Banach principal series of $p$ -adic reductive groups

Multivariable ( $φ$ , $O_{K}^{\times}$ )-modules and local-global compatibility

Conjectures and results on modular representations of $GL_{n} (K)$ for a $p$ -adic field $K$

Towards the finite slope part for $GL_{n}$