July 10, 2013 (02:45 PM PDT - 03:15 PM PDT)Speaker(s):Jaclyn Lang (Université de Paris XIII (Paris-Nord)) Location:
SLMath: Eisenbud Auditorium
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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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