Adic的不确定性：边界同调及其应用
Adic Finiteness: Bounding Homology and Applications
摘要：
我们证明了一个版本的振幅不等式的Iversen，Foxby和Iyengar，和Frankild和Sather-Wagstaff取代有限生成条件与进有限性条件。作为应用，我们证明了素特征的局部环$R$是正则的当且仅当对于某些真理想$\mathfrak b$，导出的局部上同调复形$\mathbf{R}Γ_{\mathfrak{b}}(R)$在Frobenius自同态的某些正幂下具有有限平坦维数.
英文摘要：
We prove a versions of amplitude inequalities of Iversen, Foxby and Iyengar, and Frankild and Sather-Wagstaff that replace finite generation conditions with adic finiteness conditions. As an application, we prove that a local ring $R$ of prime characteristic is regular if and only if for some proper ideal $\mathfrak b$ the derived local cohomology complex $\mathbf{R}Γ_{\mathfrak{b}}(R)$ has finite flat dimension when viewed through some positive power of the Frobenius endomorphism.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
