Special Colloquium

Anwesh Ray, Chennai Mathematical Institute

"Diophantine stability for elliptic curves on average"

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.

Zoom link: https://uwaterloo.zoom.us/j/2433704471?pwd=aXJoSDh0NDF0aFREbkthSnFBOUI4UT09