Hi everyone,
Our next NT seminar will be Anwesh Ray from Université de Montréal (CRM). Note that this talk will be virtual.
Time: Tuesday, April 25, 11am
Location: Zoom: 934 8731 7861 Passcode: C401
Title: Diophantine stability for elliptic curves on average
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.
See you there!
Masahiro