Base change along the Frobenius endomorphism and the Gorenstein property
Base change along the Frobenius endomorphism and the Gorenstein property
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DOI：
10.1016/j.jalgebra.2021.12.001
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发表时间：
2019-10
影响因子：
0.9
通讯作者：
Pinches Dirnfeld
中科院分区：
文献类型：
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作者：
Pinches Dirnfeld
设R是具有正特征的局部环，X_a复形具有非零的非生成同调和有限的内射维数。我们证明，如果X通过Frobenius（或更一般地说，通过一个收缩）自同态的派生基变化有有限的内射维数thenR是Gorenstein。特别地，我们对Falahola和Marley提出的一个问题给出了肯定的回答[7，问题3.9]。
LetRbe a local ring of positive characteristic andXa complex with nonzero finitely generated homology and finite injective dimension. We prove that if the derived base change ofXvia the Frobenius (or more generally, via a contracting) endomorphism has finite injective dimension thenRis Gorenstein. In particular, we give an affirmative answer to a question by Falahola and Marley [7, Question 3.9].