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arXiv · 1906.07215

Asymptotic Grothendieck groups and c.b.l.f. positive dg-algebras

Gregoire Naisse
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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.

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Gregoire Naisse. 2019-06-17. Asymptotic Grothendieck groups and c.b.l.f. positive dg-algebras. https://arxiv.org/abs/1906.07215

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