Resumen de 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
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).
