反向余sheaves在概形上的应用
Contraherent cosheaves on schemes
AI总结：
本文研究了概形上的反向余sheaves，构建了两种形式的导出反向余对应，并探讨了其在Noetherian概形上的应用。
摘要：
反向余sheaves是通过在概形上粘贴得到的交换环上contraadjusted或cotorsion模的全局化，使用同态函子Hom_R(S,{-})进行粘贴（其中S是SpecR中的一个仿射开子概形的函数环）。在概形上反向余sheaves的范畴是一个Quillen精确范畴，具有无限乘积的精确函子。在准紧半分离概形或Noetherian概形（在另一种版本中，任何局部Noetherian概形）上，它也有足够的投射对象。我们以两种形式构建了概形上的导出反向余对应。第一种是常规导出范畴的准相干sheaves和反向余sheaves之间的等价关系，适用于任何准紧半分离概形。更复杂的版本是准导出范畴的准相干sheaves与反向导出范畴的反向余sheaves之间的等价关系，适用于具有双倍复形的Noetherian概形。前者观点允许我们得到Lipman-Neeman非凡逆像函子f^!的显式构造，适用于准紧半分离概形之间的映射f:Y→X。后者方法提供了扩展的反向Serre-Grothendieck对偶理论，并导致Hartshorne-Deligne非凡逆像函子f^!（我们将其称为f^+）的构造，适用于有限型映射f之间的Noetherian概形。我们还构建了导出半反向半反对应，将“朴素”版本沿纤维堆叠在依赖于双倍复形的基的平展纤维上的版本之上。附录中简要讨论了非交换Noetherian堆栈、仿射Noetherian正式概形和ind-affine ind-schemes的非交换类比。
英文摘要：
Contraherent cosheaves are globalizations of contraadjusted or cotorsion modules over commutative rings obtained by gluing together over a scheme, with the colocalization functors $\operatorname{Hom}_R(S,{-})$ used for the gluing (where $S$ is the ring of functions on an affine open subscheme in $\operatorname{Spec}R$). The category of contraherent cosheaves over a scheme is a Quillen exact category with exact functors of infinite product. Over a quasi-compact semi-separated scheme or a Noetherian scheme of finite Krull dimension (in a different version - over any locally Noetherian scheme), it also has enough projectives. We construct the derived co-contra correspondence over a scheme in two forms. The "naive" one is an equivalence of the conventional derived categories of quasi-coherent sheaves and contraherent cosheaves, valid over any quasi-compact semi-separated scheme. The more sophisticated version is an equivalence between the coderived category of quasi-coherent sheaves and the contraderived category of contraherent cosheaves over a Noetherian scheme with a dualizing complex. The former point of view allows us to obtain an explicit construction of the Lipman-Neeman extraordinary inverse image functor $f^!$ for a morphism of quasi-compact semi-separated schemes $f\colon Y\to X$. The latter approach provides an expanded version of the covariant Serre-Grothendieck duality theory and leads to the Hartshorne-Deligne extraordinary inverse image functor $f^!$ (which we denote by $f^+$) for a morphism of finite type $f$ between Noetherian schemes. We also construct a derived semico-semicontra correspondence, mounting the "naive" version along the fibers on top of the one depending on a dualizing complex on the base of a flat fibration. Noncommutative analogues of Noetherian stacks, affine Noetherian formal schemes, and ind-affine ind-schemes are briefly discussed in the appendices.
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。
