Grothendieck groups and tilting objects

I. Reiten; M. Van den Bergh

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arXiv · math/0005100

Grothendieck groups and tilting objects

I. Reiten·M. Van den Bergh

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Abstract

Let C be a connected noetherian hereditary abelian Ext-finite category with Serre functor over an algebraically closed field k, with finite dimensional homomorphism and extension spaces. Using the classification of such categories from math.RT/9911242, we prove that if C has some object of infinite length, then the Grothendieck group of C is finitely generated if and only if C has a tilting object.

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BibTeX RIS

I. Reiten, M. Van den Bergh. 2000-05-10. Grothendieck groups and tilting objects. https://arxiv.org/abs/math/0005100

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