The Grothendieck Group of a Quantum Projective Space Bundle

Abstract

We compute the Grothendieck group K_0 of non-commutative analogues of quantum projective space bundles. Our results specialize to give the Grothendieck groups of non-commutative analogues of projective spaces, and specialize to recover the Grothendieck group of a usual projective space bundle over a regular noetherian separated scheme. As an application we develop an intersection theory for the quantum ruled surfaces defined by Van den Bergh.

This paper is being replaced so I can correct the metadata, the title! I (Paul) spelled Grothendieck's name incorrectly. The paper is being reposted with the journal reference and doi added to the metadata

References in corpus (2)

• Blowing up non-commutative smooth surfaces
• Serre duality for non-commutative P^1-bundles

Cited by in corpus (2)

• The geometry of points on quantum projectivizations
• Serre finiteness and Serre vanishing for non-commutative P^1-bundles