格罗滕迪克对偶理论——抽象与具体，第一部分：伪凝聚有限映射
Grothendieck Duality theories -- abstract and concrete, I: pseudo-coherent finite maps
AI总结：
本文为格罗滕迪克对偶理论半综述首部分，梳理该理论具体构造与抽象范畴论两种研究路径的关联，证明Hartshorne理想定理对诺特概形本质有限型映射及下有界拟凝聚上同调复形成立，本部分聚焦伪凝聚有限映射。
摘要：
格罗滕迪克对偶——即合适概形态射范畴上的扭曲逆像伪函子(-)^!的理论——既可以具体方式展开，侧重显式构造，也可以抽象方式展开，侧重范畴论层面的考量。目前并不清楚这两种方式导出的理论本质上是否等价。本文是半综述性的论述，探讨这两种研究路径之间的关联，这是一个涉及微分形式、留数与对偶等诸多引人关注的联系的非平凡问题。具体而言，研究表明Hartshorne所著《Residues and Duality》中核心的理想定理（Ideal Theorem），对诺特概形的任意本质有限型映射、以及具有拟凝聚上同调的下有界复形均成立。本第一部分的内容主要围绕伪凝聚有限映射展开，其余部分仍在筹备中。
英文摘要：
Grothendieck Duality -- the theory of the twisted inverse image pseudofunctor (-)^! over a suitable category of scheme-maps -- can be developed concretely, with emphasis on explicit constructions, or abstractly, with emphasis on category-theoretic considerations. It is not obvious that the two resulting theories are essentially the same. This is a semi-expository account of the connection between these approaches, a nontrivial matter involving some alluring relations, for instance among differential forms, residues and duality. In particular, it emerges that the culminating Ideal Theorem in Hartshorne's "Residues and Duality" holds for arbitrary essentially-finite-type maps of noetherian schemes and bounded-below complexes with quasi-coherent cohomology. What appears in this first part mostly concerns pseudo-coherent finite maps. The rest is being prepared.
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。
