Asymptotic Grothendieck groups and c.b.l.f. positive dg-algebras
Abstract
We introduce the notion of asymptotic Grothendieck groups for abelian and triangulated categories that are both AB4 and AB4*. We study when the asymptotic Grothendieck group of the heart of a triangulated category with a t-structure is isomorphic to the asymptotic Grothendieck group of the triangulated category itself. We also explain a connexion with the notion of topological Grothendieck group from Achar-Stroppel. Finally, we compute the asymptotic Grothendieck group of some positive (dg-)algebras having a cone bounded, locally finite dimension.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2019
- DOI:
- 10.48550/arXiv.1906.07215
- arXiv:
- arXiv:1906.07215
- Bibcode:
- 2019arXiv190607215N
- Keywords:
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- Mathematics - Category Theory;
- Mathematics - Representation Theory
- E-Print:
- v2, 66pages, with additional examples