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On images of Galois representations associated to non-CM Hida families of modular forms

New Geometric Techniques in Number Theory July 01, 2013 - July 12, 2013

July 10, 2013 (02:45PM PDT - 03:15PM PDT)
Speaker(s): Jaclyn Lang (University of California, Los Angeles)
Location: MSRI: Simons Auditorium
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Abstract In the 1980s Ribet and Momose determined the image of Galois representations associated to non-CM classical modular forms in terms of conjugate self-twists of those modular forms. Recent work of Hida shows that Galois representations associated to non-CM Hida families have large image. We define conjugate self-twists in the context of Hida families and combine the above mentioned results to obtain a description of the images of Galois representations associated to Hida families. We will attempt to motivate and introduce the local Langlands conjecture for GL(2) in families proposed by Emerton and Helm, and discuss how the classical theory of zeta integrals and local constants works in this setting.
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