報告題目：非交換奇點解消(Noncommutative quasi-resolutions of singularities)
報告時間：2019年4月23日9：00—11:00，
2019年4月25日9：00—11:00
報告地點：理科實驗中心210室
報告人：秦曉珊博士(復旦大學)
報告摘要：The notion of a noncommutative quasi-resolution is introduced fora noncommutative noetherian algebra with singularities, even for a non-CohenMacaulay algebra. If A is a commutative normal Gorenstein domain, then anoncommutative quasi-resolution of A naturally produces a noncommutativecrepant resolution (NCCR) of A in the sense of Van den Bergh, and vice versa.Under some mild hypotheses, I will talk the following results:
(1) in dimension two, all noncommutative quasi-resolutions of a given noncommutative algebra are Morita equivalent;
(2) in dimension three, all noncommutative quasi-resolutions of a given noncommutative algebra are derived equivalent.
These assertions generalize important results of Van den Bergh, Iyama-Reitenand Iyama-Wemyss in the commutative and central-finite cases.