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arXiv · 1405.1278

Cohomological Comparison Theorem

Edward Green·Dag Madsen·Eduardo N. Marcos
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Abstract

If $f$ is an idempotent in a ring $Λ$, then we find sufficient \linebreak conditions which imply that the cohomology rings $\oplus_{n\ge 0}Ext^n_Λ(Λ/{\br},Λ/{\br})$ and \linebreak $\oplus_{n\ge 0}Ext^n_{fΛf}(fΛf/f{\br} f,fΛf/f{\br} f)$ are eventually isomorphic. This result allows us to compare finite generation and GK dimension of the cohomology rings $Λ$ and $fΛf$. We are also able to compare the global dimensions of $Λ$ and $fΛf$.

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Edward Green, Dag Madsen, Eduardo N. Marcos. 2014-05-06. Cohomological Comparison Theorem. https://arxiv.org/abs/1405.1278

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