2112.09874Dec 18, 20219 pages

A note on Grothendieck groups of periodic derived categories

Shunya Saito

Abstract

We determine Grothendieck groups of periodic derived categories. In particular, we prove that the Grothendieck group of the $m$ -periodic derived category of finitely generated modules over an Artin algebra is a free $\mathbb{Z}$ -module if $m$ is even but an $\mathbb{F}_2$ -vector space if $m$

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