Cosupports and minimal pure-injective resolutions of affine rings

[摘要] We prove that any affine ring R over a field k has full cosupport, i.e., the cosupport of R is equal to Spec R. Using this fact, we give a complete description of all terms in a minimal pure-injective resolution of R, provided that vertical bar k vertical bar = aleph(1) and dim R >= 2, or vertical bar k vertical bar >= aleph(1) and dim R = 2. As a corollary, we obtain a partial answer to a conjecture by Gruson. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-15

[关键词] Support;Cosupport;Derived category