On the Stable category of maximal Cohen-Macaulay modules over Gorenstein rings-I
2021
Let $(A,\mathfrak{m})$ be a Gorenstein local ring and let $CMS(A)$ be its stable category of maximal CM $A$-modules. Suppose $CMS(A) \cong CMS(B)$ as triangulated categories. Then we show
(1) If $A$ is a complete intersection of codimension $c$ then so is $B$.
(2) If $A, B$ are Henselian and not hypersurfaces then $\dim A = \dim B$.
(3) If $A, B$ are Henselian and $A$ is an isolated singularity then so is $B$.
We also give some applications of our results.
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