交换环上的逆变有限分解子范畴
Contravariantly finite resolving subcategories over commutative rings
摘要：
有限生成模范畴的逆变有限可分解子范畴在代数的表示论中起着重要的作用。本文研究了交换环上的逆变有限分解子范畴。本文的主要目的是对Henselian Gorenstein局部环上的逆变有限分解子范畴进行分类，实际上只存在三个逆变有限分解子范畴。我们的方法，以获得这种分类也恢复作为一个副产品的定理克里斯滕森，Piepmeyer，Striuli和高桥有关的关系之间的逆变有限性的满子范畴的全自反模和Gorenstein性质的基环。
英文摘要：
Contravariantly finite resolving subcategories of the category of finitely generated modules have been playing an important role in the representation theory of algebras. In this paper we study contravariantly finite resolving subcategories over commutative rings. The main purpose of this paper is to classify contravariantly finite resolving subcategories over a henselian Gorenstein local ring; in fact there exist only three ones. Our method to obtain this classification also recovers as a by-product the theorem of Christensen, Piepmeyer, Striuli and Takahashi concerning the relationship between the contravariant finiteness of the full subcategory of totally reflexive modules and the Gorenstein property of the base ring.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
