Iterated Mapping Cones on the Koszul Complex and Their Application to Complete Intersection Rings

Autor:	Nguyen, Van C., Veliche, Oana
Rok vydání:	2022
Předmět:	Mathematics - Commutative Algebra Mathematics - K-Theory and Homology Mathematics - Rings and Algebras 13D02 13D07 13H10 18G10 18G35
Druh dokumentu:	Working Paper
Popis:	Let $(R,\mathfrak m, \mathsf k)$ be a complete intersection local ring, $K$ be the Koszul complex on a minimal set of generators of $\mathfrak m$, and $A=H(K)$ be its homology algebra. We establish exact sequences involving direct sums of the components of $A$ and express the images of the maps of these sequences as homologies of iterated mapping cones built on $K$. As an application of this iterated mapping cone construction, we recover a minimal free resolution of the residue field $\mathsf k$ over $R$, independent from the well-known resolution constructed by Tate by adjoining variables and killing cycles. Through our construction, the differential maps can be expressed explicitly as blocks of matrices, arranged in some combinatorial patterns. Comment: To appear in Journal of Algebra and its Applications (19 pages)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.02606 Zobrazit plný text záznamu View this record from Arxiv