标题： Silt降低，相对AGK构造和Higgs构造 显示英文标题

标题： Silting reduction, relative AGK's construction and Higgs construction

摘要： 我们引入了Calabi--Yau四元组的概念，作为Iyama--Yang的Calabi--Yau三元组的推广。对于每个\((d+1)\)-Calabi--Yau四元组，我们证明相关的Higgs范畴是一个\(d\)-Calabi--Yau Frobenius extriangulated范畴，而且还包含一个规范的\(d\)-簇-tilting子范畴。具体的例子来自于冰quiver带势能设置下的相对簇范畴和Higgs范畴的构造，以及孤立奇点的奇点范畴。作为应用，我们证明了相对Amiot--Guo--Keller的构造和\((d+1)\)-Calabi--Yau四元组的Higgs构造都将silt减少到Calabi--Yau减少。 显示英文摘要

摘要： We introduce the notion of a Calabi--Yau quadruple as a generalization of Iyama--Yang's Calabi--Yau triple. For each \((d+1)\)-Calabi--Yau quadruple, we show that the associated Higgs category is a \(d\)-Calabi--Yau Frobenius extriangulated category, which moreover admits a canonical \(d\)-cluster-tilting subcategory. Concrete examples arise from the construction of relative cluster categories and Higgs categories in the setting of ice quivers with potentials, as well as from the singularity category of an isolated singularity. As an application, we prove that both the relative Amiot--Guo--Keller's construction and the Higgs construction of a \((d+1)\)-Calabi--Yau quadruple take silting reduction to Calabi--Yau reduction.