Let $(A,\mathfrak{m}), (B,\mathfrak{n}) $ be Gorenstein local rings and let $\underline{CM}(A)$ be its stable category of finitely generated maximal Cohen-Macaulay $A$-modules. Suppose we have an equivalence $\Phi \colon\underline{CM}(A) \rightarrow \underline{CM}(A)$ as triangulated categories. We show (1) If $A, B$ a...
Let $(A,\mathfrak{m})$ be a Cohen-Macaulay local ring of dimension $d$, residue field $k$ and let $I$ be an $\mathfrak{m}$-primary ideal. Assume $k$ is infinite. Let $N$ be a perfect $A$-module of dimension $t \geq 1$. Let $M$ be a MCM $A$-module. The function $n \rightarrow \ell(\text{Tor}^A_j(M, N/I^{n+1}N))$ is of p...
Let $(A,\mathfrak{m})$ be a Cohen-Macaulay local ring of dimension $d$ and residue field $k$. Let $M$ be a maximal Cohen-Macaulay $A$-module. Let $e(M)$ be the multiplicity of $M$ and let $\mu(M)$ denote the number of its minimal generators. (1) Assume $A$ is not a complete intersection. If $\text{curv}(M)<\text{curv}(...
Let $(A,\mathfrak{m})$ be a Noetherian local ring of dimension $d$ and let $M$ be a finitely generated $A$-module. Assume $M$ has rank $r>0$. We show that if $M$ is NOT Cohen-Macaulay then $\mu_d(\mathfrak{m}, M)>r$. If further $A$ is unmixed and $\mu_n(\mathfrak{m}, M) \leq 1$ for some $n \geq d$ then we prove $\text{...
Tony J. Puthenpurakal· 0 citations
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