Images of adelic Galois representations for modular forms

Abstract

We show that the image of the adelic Galois representation attached to a non-CM modular form is open in the adelic points of a suitable algebraic group. We also show a similar result for the adelic Galois representation attached to a finite set of modular forms.

Updated version, to appear in Glasgow J Math

References in corpus (2)

• Rankin--Eisenstein classes and explicit reciprocity laws
• On the Brauer class of Modular Endomorphism Algebras

Cited by in corpus (12)

• Rankin--Eisenstein classes and explicit reciprocity laws
• Rankin--Eisenstein classes in Coleman families
• Euler systems for Hilbert modular surfaces
• Iwasawa theory for Rankin--Selberg products of $p$-non-ordinary eigenforms
• Main conjectures for higher rank nearly ordinary families -- I
• Iwasawa theory of twists of elliptic modular forms over imaginary quadratic fields at inert primes
• Multiplicity of Eisenstein series in cohomology and applications to $GS{p}_4$ and $G_2$
• Supercuspidal ramifications and traces of adjoint lifts at good primes
• Divisors of Fourier coefficients of two newforms
• Bounding Selmer groups for the Rankin--Selberg convolution of Coleman families
• On the semisimplicity of reductions and adelic openness for $E$-rational compatible systems over global function fields
• Modular forms of arbitrary even weight with no exceptional primes