The leading constant for rational points in families
arXiv:2210.13559
Abstract
We prove asymptotics for Serre's problem on the number of diagonal planar conics with a rational point and use this to put forward a new conjecture on counting the number of varieties in a family which are everywhere locally soluble.
52 pages, comments welcome. Slightly modified definition of the subordinate Brauer group and Tamagawa volume of the Brauer-Manin set