AI 中文总结
利用伊古萨层和法尔格斯 - 肖尔策工作，研究PEL型AC极小紧化志村簇相交上同调，构造特定层并证明其性质，得出相交上同调相关应用，还研究了分层间相互作用及反常\(t\)-结构。
AI 中文摘要
我们利用伊古萨层和法尔格斯 - 肖尔策的工作研究了PEL型AC的极小紧化志村簇的相交上同调。具体而言，我们在法尔格斯 - 方丹曲线上的\(G\)-丛的模层上构造了一个层，在几何朗兰兹意义下应用一个赫克算子后能恢复此相交上同调。我们证明该层有若干良好性质，如Verdier自对偶和反常层性质。这导致了相交上同调的若干应用，包括曼托万积公式的一个版本以及挠消失和艾希勒 - 志村关系。在此过程中，我们研究了极小紧化伊古萨层上贝利 - 博雷尔分层与牛顿分层之间的相互作用，并研究了分层\(v\)-层上的反常\(t\)-结构。
英文摘要
We study the intersection cohomology of minimally compactified Shimura varieties of PEL type AC using Igusa stacks and the work of Fargues-Scholze. More precisely, we construct a sheaf on the moduli stack of $G$-bundles on the Fargues-Fontaine curve, which recovers this intersection cohomology after applying a Hecke operator in the sense of geometric Langlands. We show that this sheaf has several desirable properties; for example, it is Verdier self-dual and perverse. This leads to several applications to intersection cohomology, including a version of the Mantovan product formula, as well as torsion-vanishing and Eichler-Shimura relations. Along the way, we investigate the interaction between Baily-Borel and Newton stratifications on minimally compactified Igusa stacks, and we study perverse t-structures on stratified v-stacks.
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