Commutative Algebra and its Interactions A conference in honor of Mel Hochster July 31 - August 5, 2008 Abstract Detail   Title: Vanishing of Tor and torsion-freeness of the divisor class groups We show that if R = S/(f) is a local hypersurface of an unramified regular local ring S, such that dim R =3 and R has isolated singularity, then the class group of R is torsion-free. This work is motivated by a conjecture of Gabber stating that for any Hensenlian, local, complete intersection R of dimension 3, the Picard group of the punctured spectrum of R is torsion-free. The proof use a function on the Grothendieck group of R defined by Hochster. Hailong Dao University of Utah Email:  hdao@math.utah.edu Phone:   BACK to Speaker Listing BACK to Conference Home