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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)

- 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)

- Ana Caraiani, Florian Herzig, Brian Conrad
- 2015

Ana Caraiani, "On the p-adic local Langlands correspondence for GL2(Qp) and beyond" The p-adic local Langlands program is a recent generalization of the classical Langlands program and appears to be the natural context in which to study the latter. In this talk, I will start by talking about relating two-dimensional Galois representations and modular forms,… (More)

- Toby Gee, Florian Herzig, TOBY GEE, Mark Kisin
- 2009

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)

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)

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)