منابع مشابه
Modularity lifting theorems for ordinary Galois representations
We generalize the results of [CHT08] and [Tay08] by proving modularity lifting theorems for ordinary l-adic Galois representations of any dimension of a CM or totally real number field F . The main theorems are obtained by establishing an R = T theorem over a Hida family. A key part of the proof is to construct appropriate ordinary lifting rings at the primes dividing l and to determine their i...
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An elliptic curve over a field K is a projective nonsingular genus 1 curve E over K along with a chosen K-rational point O of E, which automatically becomes an algebraic group with identity O. If K has characteristic 0, the n-torsion of E, denoted E[n], is isomorphic to (Z/nZ) over K. The absolute Galois group GK acts on these points as a group automorphism, hence it acts on the inverse limit l...
متن کاملOctahedral Galois Representations Arising from Q-curves of Degree 2
Generically, one can attach to a Q-curve C octahedral representations ρ : Gal(Q/Q) −→ GL 2 (F 3) coming from the Galois action on the 3-torsion of those abelian varieties of GL 2-type whose building block is C. When C is defined over a quadratic field and has an isogeny of degree 2 to its Galois conjugate, there exist such representations ρ having image into GL 2 (F 9). Going the other way, we ...
متن کاملModularity Lifting Theorems for Galois Representations of Unitary Type
We prove modularity lifting theorems for l-adic Galois representations of any dimension satisfying a unitary type condition and a Fontaine-Laffaille type condition at l. This extends the results of Clozel, Harris and Taylor ([CHT08]), and the subsequent work by Taylor ([Tay08]). The proof uses the Taylor-Wiles method, as improved by Diamond, Fujiwara, Kisin and Taylor, applied to Hecke algebras...
متن کاملGalois representations which are not minimally elliptic
In a recent preprint (see [C]), F. Calegari has shown that for l = 2, 3, 5 and 7 there exist 2-dimensional irreducible representations ρ of Gal(Q̄/Q) with values in Fl coming from the l-torsion points of an elliptic curve defined over Q, but not minimally, i.e., so that any elliptic curve giving rise to ρ has prime-to-l conductor greater than the (prime-to-l) conductor of ρ. In this brief note, ...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 1996
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.1996.v3.n3.a4