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Local imprimitivity of points on elliptic curves

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Peter Stevenhagen
Leiden University/MPIM
Wed, 30/11/2022 - 14:30 - 15:30
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Contact: Pieter Moree (

An element in a number field K that is primitive, i.e., not a k-th power for k>1, is a primitive root modulo infinitely many primes of K, at least under GRH. Primitive points on elliptic curves E/K may fail to have this reasonable property even in cases where E has infinitely many primes of cyclic reduction. We discuss the `anomalous' behaviour of the Galois representations underlying the failure of this local-global principle.
This concerns joint work (at MPIM) with Francesco Campagna and Francesco Pappalardi.


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