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

    1. [1] Indian Institute of Technology Bombay- INDIA
  • Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 120, Nº 2, 2017, págs. 161-180
  • Idioma: inglés
  • Texto completo no disponible (Saber más ...)
  • Resumen
    • Let (A,m) be a Gorenstein local ring of dimension d≥1. Let CM−−−(A) be the stable category of maximal Cohen-Macauley A-modules and let ICM−−−−(A) denote the set of isomorphism classes in CM−−−(A). We define a function ξ:ICM−−−−(A)→Z which behaves well with respect to exact triangles in CM−−−(A). We then apply this to (Gorenstein) liaison theory. We prove that if dimA≥2 and A is not regular then the even liaison classes of {mn∣n≥1} is an infinite set. We also prove that if A is Henselian with finite representation type with A/m uncountable then for each m≥1 the set Cm={I∣I is a codim 2 CM-ideal with e0(A/I)≤m} is contained in finitely many even liaison classes L1,…,Lr (here r may depend on m).


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