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 A ≥ 2 and A is not regular then the even liaison classes of { m^n 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 C_m = { I I is a codim 2 CM-ideal with e_0(A/I) ≤ m } is contained in finitely many even liaison classes L_1,… ,L_r (here r may depend on m). , number=2, journal=MATHEMATICA SCANDINAVICA, author=Puthenpurakal, Tony J., year=2017, month=May, pages=161–180