Strong approximation for the intersection of two quadrics

Abstract

We study strong approximation for the intersection of two affine quadrics. As its application, we prove the fibration method for weak approximation over number fields of rank four with nonsplit fibers split by quadratic extensions.

There is an error in the proof of Property 4.3 in the previous version. This makes certain results related to Conjecture F+ difficult to prove. For this reason, all sections concerning multiple fibers have been removed from this version. Although the results on toric varieties presented in Section 9 are right, they have also been deleted