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arXiv · 1801.04476

Cosupports and minimal pure-injective resolutions of affine rings

Tsutomu Nakamura
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Abstract

We prove that any affine ring $R$ over a field $k$ has full cosupport, i.e., the cosupport of $R$ is equal to ${\rm Spec}\, R$. Using this fact, we give a complete description of all terms in a minimal pure-injective resolution of $R$, provided that $|k|=\aleph_1$ and ${\rm dim}\, R\geq 2$, or $|k|\geq \aleph_1$ and ${\rm dim}\, R=2$. As a corollary, we obtain a partial answer to a conjecture by Gruson.

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Tsutomu Nakamura. 2018-01-13. Cosupports and minimal pure-injective resolutions of affine rings. https://arxiv.org/abs/1801.04476

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