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- FLORIAN HERZIG
- 2006

We formulate a Serre-type conjecture for n-dimensional Ga-lois representations that are tamely ramified at p. The weights are predicted using a representation-theoretic recipe. For n = 3 some of these weights were not predicted by the previous conjecture of Ash, Doud, Pollack, and Sinnott. Computational evidence for these extra weights is provided by… (More)

- FLORIAN HERZIG
- 2009

Let F be a finite extension of Qp. Using the mod p Sa-take transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive group over Fp to be supersingular. We then give the classification of irreducible admissible smooth GLn(F)-representations over Fp in terms of supersingular representations. As a… (More)

- FLORIAN HERZIG
- 2010

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 over the algebraic closure of the residue field of F. We establish an analogue of the Sa-take isomorphism for the Hecke algebra of compactly supported, K-biequivariant functions f :… (More)

- Christophe Breuil, Florian Herzig
- 2012

- F. Herzig, J. Tilouine
- 2011

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 (in the symplectic sense). The modu-larity condition is formulated using thé etale and the algebraic de Rham cohomology of Siegel modular varieties of level prime to p. We… (More)

The notion of adequate subgroups was introduced by Jack Thorne [59]. It is a weakening of the notion of big subgroups used by Wiles and Taylor in proving auto-morphy lifting theorems for certain Galois representations. Using this idea, Thorne was able to strengthen many automorphy lifting theorems. It was shown in [22] and [23] that if the dimension is… (More)

- Toby Gee, Florian Herzig, TOBY GEE
- 2009

The notion of adequate subgroups was introduced by Jack Thorne [42]. It is a weakening of the notion of big subgroups used in generalizations of the Taylor-Wiles method for proving the automorphy of certain Galois representations. Using this idea, Thorne was able to strengthen many automorphy lifting theorems. It was shown in [22] that if the dimension is… (More)

- MATTHEW EMERTON, FLORIAN HERZIG
- 2013

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 representation which is irre-ducible when restricted to each decomposition group above p are exactly those previously predicted by the third author. We do this by combining explicit… (More)

Let l be a prime, and let Γ be a finite subgroup of GL n (F l) = GL(V). With these assumptions we say that Condition (C) holds if for every irreducible Γ-submodule W ⊂ ad 0 V there exists an element g ∈ Γ with an eigenvalue α such that tr e g,α W = 0. Here, e g,α denotes the projection to the generalised α-eigenspace of g. This condition arises in the… (More)