منابع مشابه
MOD p REPRESENTATIONS ON ELLIPTIC CURVES
Modular Galois representations ρ : Gal(Q/Q) → GL2(Fp) with cyclotomic determinant arise from elliptic curves for small p. We show that ρ does not necessarily arise from an elliptic curve whose conductor is as small as possible outside p. For p = 3 this disproves a conjecture of J. Lario and A. Rio [8].
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In this paper, we will use techniques of Conrey, Farmer and Wallace to find spaces of modular forms Sk(Γ0(N)) where all of the eigenspaces have Hecke eigenvalues defined over Fp, and give a heuristic that these are all such spaces.
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Let F be a finite extension of Qp. Using the mod p Satake 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 consequence we deduce that supersingular...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2013
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2012.09.010