Syzygies of ideals of polynomial rings over principal ideal domains

Abstract

We study computational aspects of syzygies of graded modules over polynomial rings R[w1, ..., wg] when the base R is a discrete valuation ring. In particular, we use the torsion of their syzygies over R to provide a formula which describes the behavior of the Betti numbers when changing the base to the residue field or the fraction field of R. Our work is motivated by the deformation theory of curves.