The Monomial Conjecture and order ideals II

2015/06/21 by S. P. Dutta, Dutta, S. P.
Mathematics · #13D22 #13D25 #13H05 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Primary: 13D02 #Secondary: 13C15

paper · pdf · doi:10.48550/arxiv.1506.06420

openalex publication_date 2015/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let I be an ideal of height d in a regular local ring (R,m,k=R/m) of dimension n and let Ω denote the canonical module of R/I. In this paper we first prove the equivalence of the following: the non-vanishing of the edge homomorphism η_d: \extRn-dk,Ω → \extRnk,R, the validity of the order ideal conjecture for regular local rings, and the validity of the monomial conjecture for all local rings. Next we prove several special cases of the order ideal conjecture/monomial conjecture.

Related

• On a Consequence of the Order Ideal Conjecture
• Order Ideals and a Generalized Krull Height Theorem
• Monomial ideals with regular quotients and some edge rings
• Huneke-Wiegand conjecture and change of rings
• Local cohomology of ideals and the R_n condition of Serre