Anwesh Ray, Université de Montréal
Tuesday, April 25, 2023 - 11:00am to 12:00pm
Virtual
Abstract:
Let K be a number field and ℓ≥ 5 be a prime number. Mazur and Rubin introduced the notion of diophantine stability for a variety X/K at a prime ℓ. Under the hypothesis that all elliptic curves E/ℚ have finite Tate-Shafarevich group, we show that there is a positive density set of elliptic curves E/ℚ of rank 1, such that E/K is diophantine stable at ℓ. This result has implications to Hilbert's tenth problem for number rings. This is joint work with Tom Weston.