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

Abstract

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 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 calculations of Doud and Pollack. We obtain theoretical evidence for n = 4 using automorphic inductions of Hecke characters.

68 pages, revised (mainly added appendix that generalises Jantzen's theorem on the reduction modulo p of Deligne--Lusztig representations)

References in corpus (2)

• On Serre's conjecture for mod l Galois representations over totally real fields
• Conjecture de type de Serre et formes compagnons pour GSp_4

Cited by in corpus (42)

• On Serre's conjecture for mod l Galois representations over totally real fields
• The classification of irreducible admissible mod p representations of a p-adic GL_n
• A Satake isomorphism in characteristic p
• Weight cycling and Serre-type conjectures for unitary groups
• Companion forms for unitary and symplectic groups
• Ordinary representations of G(Q_p) and fundamental algebraic representations
• On mod p local-global compatibility for GL_3 in the ordinary case
• Diagrams in the mod $p$ cohomology of Shimura curves
• On defining characteristic representations of finite reductive groups
• Serre Weights for U(n)
• Weight elimination in Serre-type conjectures
• p-adic Hodge-theoretic properties of étale cohomology with mod p coefficients, and the cohomology of Shimura varieties
• Multiplicity one at full congruence level
• Sur la torsion dans la cohomologie des variétés de Shimura de Kottwitz-Harris-Taylor
• Modules universels de GL(3) sur un corps p-adique en caractéristique p
• Multiplicity one for wildly ramified representations
• The weight reduction of mod $p$ Siegel modular forms for $GS{p}_4$
• Moduli stacks of étale (phi,Gamma)-modules and the existence of crystalline lifts
• Automorphic lifts of prescribed types
• Serre weight conjectures for $p$-adic unitary groups of rank 2
• On endomorphism algebras of Gelfand-Graev representations II
• Serre weights and Breuil's lattice conjecture in dimension three
• Serre weights for $GS{p}_4$ over totally real fields
• Non-admissible irreducible representations of $p$-adic ${\mathrm{GL}}_n$ in characteristic $p$
• Potentially crystalline deformation rings and Serre weight conjectures
• Moduli of Fontaine--Laffaille representations and a mod-$p$ local-global compatibility result
• Lattices in the cohomology of $U(3)$ arithmetic manifolds
• Reducible Galois representations and the homology of GL(3,Z)
• On the universal module of $p$-adic spherical Hecke algebras
• On mod $p$ local-global compatibility for ${\mathrm{GL}}_n({\mathbf{Q}}_p)$ in the ordinary case
• Serre weights for three-dimensional wildly ramified Galois representations
• Gelfand-Kirillov dimension and mod p cohomology for GL2
• Test vectors for some ramified representations
• Inverse Satake isomorphism and change of weight
• Crystalline liftings and weight part of Serre's conjecture
• Serre's Modularity Conjecture
• Hecke modules and supersingular representations of U(2,1)
• Mod 2 homology for GL(4) and Galois representations
• The first pro-$p$-Iwahori cohomology of mod-$p$ principal series for $p$-adic ${\text{GL}}_n$
• Cohomology with twisted one-dimensional coefficients for congruence subgroups of SL(4,Z) and Galois representations
• On the mod $p$ cohomology for ${\mathrm{GL}}_2$: the non-semisimple case
• Even Galois representations and the cohomology of GL(2,Z)