Contravariantly finite resolving subcategories over commutative rings

Details Contravariantly finite resolving subcategories over commutative rings Contravariantly finite resolving subcategories over commutative rings

2010-02-02

arxiv.org/abs/1002.0522v1

Mathematics

Commutative Algebra

18 pages, to appear in American Journal of Mathematics

Scientific paper

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.

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