半局部情形下的Macdonald对偶及其在局部同调与局部上同调中的应用
Macdonald dual in the semilocal case and applications to local homology and local cohomology
AI总结：
本文将Macdonald对偶理论与Cuong-Nam局部同调理论推广到带J-adic拓扑的半局部诺特环，通过相关理论克服半局部情形的结构障碍，建立拓扑极限同构并关联两类同调，为推广经典结果提供基础工具。
摘要：
本文将Macdonald对偶理论以及Cuong-Nam局部同调理论（在某种意义上与A. Grothendieck的局部上同调理论[Gro1]对偶）推广到配备J-adic拓扑的半局部诺特环。通过利用Zöschinger结构理论和半局部Matlis对偶克服半局部情形的关键结构障碍，该研究建立了拓扑极限同构，并将局部同调与局部上同调关联起来。最终，该框架提供了将Macdonald[Mac]和Cuong-Nam[C-N1]的经典结果推广到半局部情形所需的基础工具。
英文摘要：
This paper extends Macdonald's duality theory and Cuong-Nam's local homology theory -- which is in some sense dual to the local cohomology theory of A. Grothendieck [Gro1] -- to semilocal noetherian rings equipped with the $J$-adic topology. By overcoming the key structural obstructions of the semilocal setting via Zöschinger's structure theory and semilocal Matlis duality, this work establishes topological limit duality isomorphisms and links local homology with local cohomology. Ultimately, this framework provides the foundational machinery required to extend the classical results of Macdonald [Mac] and Cuong-Nam [C-N1] to the semilocal setting.
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。
