### Serre's uniformity conjecture for elliptic curves with a rational cyclic isogeny

Linfoot Number Theory Seminar

8th November 2017, 11:00 am – 12:00 pm

Howard House, 2nd Floor Seminar Room

Serre’s uniformity conjecture asks if, for any elliptic curve E over the rationals without complex multiplication, its residual mod l representation is surjective for all primes l > 37. In this talk, I will show how an argument of Darmon and Merel — which is, itself, based on Mazur’s formal immersion technique — can be adapted to prove the conjecture when E admits a non-trivial cyclic isogeny.

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