A local-global principle for weak approximation on varieties over function fields

Mike Roth, Jason Michael Starr

Published 2009-08-01, updated 2009-09-04Version 2

We present a new perspective on the weak approximation conjecture of Hassett and Tschinkel: formal sections of a rationally connected fibration over a curve can be approximated to arbitrary order by regular sections. The new approach involves the study of how ideal sheaves pullback to Cartier divisors.