STNB2024(37th edition)
Automorphy of $Sim^5(GL(2))$ and refinement of the base-change proof for GL(2)
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Abstract
We provide a summary of the main ideas and facts used in Dieulefait´s 2015 paper which proved that given a Hecke eigenform of level 1, the 5-th symmetric power of the corresponding Deligne representation is automorphic and how this result can be exploited to simplify the proof disclosed in the first three talks, as well as these new ideas can be exploited to establish the automorphy of other instances of functorial operations on modular Galois representations.
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