构建栈覆叠的数据
Building Data for Stacky Covers
AI总结：
该研究定义了栈覆叠的栈构建数据，证明其与栈覆叠的(2,1)-范畴等价，指出栈覆叠为平坦根栈并给出内蕴描述，还推广了双有理构建数据对应驯分歧覆叠的判别准则。
摘要：
我们秉承Pardini的思路定义了栈覆叠的栈构建数据，并给出了栈覆叠范畴与栈构建数据范畴之间的(2,1)-范畴等价关系。我们证明了每一个栈覆叠都是Olsson以及Borne–Vistoli意义下的平坦根栈，并利用栈构建数据给出了其作为根栈的内蕴描述。当基概形S定义在一个域上时，我们给出了一个双有理构建数据源自有限阿贝尔群概形的驯分歧覆叠的判别准则，推广了Biswas–Borne的一个结果。
英文摘要：
We define stacky building data for stacky covers in the spirit of Pardini and give an equivalence of (2,1)-categories between the category of stacky covers and the category of stacky building data. We show that every stacky cover is a flat root stack in the sense of Olsson and Borne--Vistoli and give an intrinsic description of it as a root stack using stacky building data. When the base scheme S is defined over a field, we give a criterion for when a birational building datum comes from a tamely ramified cover for a finite abelian group scheme, generalizing a result of Biswas--Borne.
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