STNB2024(37th edition)
Second half of the proof of base change over Q: weight modifications and connecting with a CM form
Presenters
Javier Guillán Rial
Abstract
In this session we will finish the proof of Langlands base change over Q. For this we are going to connect the modular form we obtained in the previous session with another form (via weight modifications and minor level adjustements) whose space of cusp forms is connected by the Galois action (which of course, preserves modularity). The idea is then to build a chain of "safe" congruences from this modular form of a fixed space, to a representation attached to a CM form, in which base change is known.
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