Abstract: In his pioneering paper, Ribet uses Eisenstein congrunces to prove the converse to Herbrand's theorem. A key ingredient in his proof is the so-called Ribet's lemma of constructing nontrivial extensions of certain characters. In my talk, I will go over Ribet's lemma and its various generalizations (due to Bellaiche and Urban). In particular, I will define symplectic extension graphs associated with symplectic representations, and study it by the use of Bruhat--Tits buildings associated with symplectic groups. We obtain a generalization of Urban's result and a symplectic analogue of the result of Bellaiche.
Event Date
2026-09-16
Event Time
03:45 pm ~ 05:00 pm
Event Location
TBA