@article{Puthenpurakal_2017, title={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}, volume={120}, url={https://www.mscand.dk/article/view/25728}, DOI={10.7146/math.scand.a-25728}, abstractNote={<p>Let $(A,\mathfrak{m})$ be a Gorenstein local ring of dimension $d \geq 1$. Let $\operatorname{\underline{CM }(A)$ be the stable category of maximal Cohen-Macauley $A$-modules and let $\operatorname{\underline{ICM }(A)$ denote the set of isomorphism classes in $\operatorname{\underline{CM }(A)$. We define a function $\xi \colon \operatorname{\underline{ICM }(A) \to \mathbb{Z}$ which behaves well with respect to exact triangles in $\operatorname{\underline{CM }(A)$. We then apply this to (Gorenstein) liaison theory. We prove that if $\dim A \geq 2$ and $A$ is not regular then the even liaison classes of $\{\,\mathfrak{m}^n \mid n\geq 1 \,\}$ is an infinite set. We also prove that if $A$ is Henselian with finite representation type with $A/\mathfrak{m}$ uncountable then for each $m \geq 1$ the set $\mathcal {C}_m = \{\, I \mid I \text { is a codim $2$ CM-ideal with } e_0(A/I) \leq m \,\}$ is contained in finitely many even liaison classes $L_1,\dots ,L_r$ (here $r$ may depend on $m$).</p>}, number={2}, journal={MATHEMATICA SCANDINAVICA}, author={Puthenpurakal, Tony J.}, year={2017}, month={May}, pages={161–180} }