Vector bundles on the projective line and finite domination of chain   complexes
  Finitely dominated chain complexes over a Laurent polynomial ring in one indeterminate are characterised by vanishing of their Novikov homology. We present an algebro-geometric approach to this result, based on extension of chain complexes to sheaves on the projective line. We also discuss the K-theoretical obstruction to extension. 
Thomas Huettemann
math.AT math.KT