Speaker：Qing Liu (University of Bordeaux)

Time：2023-6-12, 9:00

Location：Conference Room 110 at Experiment Building at Haiyun Campus

Abstract:

Let X be a projective scheme over an affine scheme S. In a joint work with Gabber and Lorenzini we prove that for any closed subset F of X quasi-finite over S, there exist  hypersurfaces of X avoiding F. As an application we will prove that any projective module over a (commutative) ring A becomes a direct sum of rank 1 projective modules after a finite faithfully flat extension of A.