The elliptic sieve and Brauer groups

Appears in collection : Skorobogatov 60

A famous theorem of Serre states that almost all plane conics over Q have no rational point, when ordered by the size of their coefficients. In this talk we consider analogues of this result for families of conics parametrised by elliptic curves. This is joint work with Subham Bhakta, Simon Rydin Myerson, and Masahiro Nakahara.