STNB2025 (38th edition)
“Safe chains” and some results on Langlands’ base change
Presenters
Javier Guillán Rial
Abstract
A congruence between two Galois representations over a totally real field F is said to be “safe” if it preserves modularity. Safe congruences may be concatenated to form “safe chains”, which can be used to show the modularity or some instances of Langlands’ functoriality. In this talk we will illustrate this method with some important examples (such as the modern proof of Serre’s conjecture) and some recent developments of Langlands’ base change for totally real quadratic number fields of narrow class number one.
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