Tilting modules over small Dedekind domains

Abstract

A Dedekind domain R is called small if card( R)⩽2 ω and card(Spec( R))⩽ ω. Assuming Gödel's Axiom of Constructibility ( V= L), we characterize tilting modules over small Dedekind domains. In particular, we prove that under V= L, a class of modules, T , is a tilting torsion class iff there is a set P⊆Spec( R) such that T={M∈ Mod−R | Ext R 1(R/p,M)=0 for all p∈P} .