A function on the the set of isomorphism classes in the stable category\n of maximal Cohen-Macaulay modules over a Gorenstein ring: with applications\n to Liason theory

2013/07/10 by Tony J. Puthenpurakal, Puthenpurakal, Tony J.
Mathematics · #13D40 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 13C40 #Secondary 13C14

paper · pdf · doi:10.48550/arxiv.1307.2728

openalex publication_date 2013/07/10 · openalex created_date 2022/09/12 · openalex updated_date 2026/07/28

Abstract

Let (A, m) be a Gorenstein local ring of dimension d \≥ 1. Let\n CMS(A) be the stable category of maximal CM A-modules and let\n ICMS(A) denote the set of isomorphism classes in CMS(A). We define a\nfunction \ξ colon ICMS(A) rt ZZ which behaves well with respect to exact\ntriangles in CMS(A). We then apply this to (Gorenstein) liason theory. We\nprove that if \dim A \≥ 2 and A is not regular then the even liason\nclasses of mⁿ; n\≥ 1 is an infinite set. We also prove that if A is an\ncomplete equi-characteristic simple singularity with A/ m uncountable then\nfor each m \≥ 1 the set \C_m = I \| I \is a codim 2\nCM-ideal with e₀(A/I) \≤ m is contained in finitely many even liason\nclasses L₁,\…,L_r (here r may depend on m).\n

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