STNB2024(37a edició)
Potentially diagonalisable modular lifts of large weights and supercuspidal modular lifts of weight 2
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Resumen
In this talk, on one hand, I will prove that for a Hecke cuspform f and a prime p>6 coprime to the level, there exists an infinite family of potentially diagonalisable modular lifts of the residual Deligne representation attached to f. On the other hand, I will describe how we have adapted our method to establish the existence of supercuspidal lifts of weight 2 with a view to produce so-called "safe-chains" of modular forms which allow to prove some instances of Langlands based-change. This is joint work with Luis Dieulefait ([1],[2]).
[1] I. Blanco-Chacón, L. Dieulefait, Potentially diagonalizable modular lifts of large weight, Journal of Number Theory, Volume 228, 2021.
[2] I. Blanco-Chacón, L. Dieulefait. Modular supercuspidal lifts of weight 2. Preprint: https://arxiv.org/pdf/2310.11522.pdf
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