Frobenius functors, stable equivalences and K-theory of Gorenstein projective modules
报告人：任伟教授（重庆师范大学）
报告时间：2022年4月15日10：00-11：00
腾讯会议号：478-608-093
会议链接：
https://meeting.tencent.com/dm/iEe5eImWVvca
摘要：
Owing to the difference in K-theory, an example by Dugger and Shipley implies that the equivalence of stable categories of Gorenstein projective modules should not be a Quillen equivalence. We give a sufficient and necessary condition such that the Frobenius pair of faithful functors between two abelian categories is a Quillen equivalence, which is equivalent to that the Frobenius functors induce mutually inverse equivalences between stable categories of Gorenstein projective objects.
We show that the category of Gorenstein projective objects is a Waldenhausen category, then Gorenstein K-groups are introduced and characterized. As applications, we show that stable equivalences of Morita type preserve Gorenstein K-groups, CM-finite and CM-free. Two specific examples are presented to illustrate our results, where Gorenstein K_0 and K_1-groups are calculated.
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