Obstructions to the Hasse principle in families

TL;DR

This paper investigates conditions under which almost all members of a family of varieties over a number field do not have a Brauer-Manin obstruction to the Hasse principle, highlighting when the principle holds generically.

Contribution

It provides criteria ensuring that in a family of varieties, the Brauer-Manin obstruction is absent for nearly all members, advancing understanding of the Hasse principle in families.

Findings

Almost all family members lack Brauer-Manin obstruction

Conditions for the generic validity of the Hasse principle

Quantitative measure of obstruction absence in families

Abstract

For a family of varieties over a number field, we give conditions under which 100% of members have no Brauer-Manin obstruction to the Hasse principle.