Tuesday, April 29, 14:00, online.

Norihiro Hanihara (Kyushu University)
Reflexive modules and Auslander-Gorenstein rings.

Abstract:
Motivated by the theory of non-commutative resolutions and the results on Auslander correspondence, we study the category of reflexive modules over (commutative or non-commutative) Noetherian rings. One well-established sufficient condition for this category to behave well is that the ring should be (commutative) normal. We will explain that these nice behaviors are governed by the Auslander-type conditions which are some requirements on the minimal injective resolution of the ring. We will also discuss a Morita-type result characterizing the category of reflexive modules.