STNB2024(37a edició)
Preliminary facts and a (detailed) overview of the proof
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Resumen
In this first session we state the problem of the Langlands base change for a modular representation to a totally real number field. We start discussing the CM case and the quadratic case, via the Doi-Naganuma lifting. Next, after mentioning the general solvable (hence abelian case), we comment the Hida-Maeda approach to the non-abelian case. Next, we provide an overview of Dieulefait´s proof step by step discussing how some of the hypotheses can be waived in a further 2015 result . Finally, we start the first step of the proof, commenting Kisin´s core result and reducing to a weight 2 situation.
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