Building data for stacky covers

• Eric Ahlqvist ^[1]
  1. [1] University of Edinburgh

     University of Edinburgh

     Reino Unido

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 3, 2024, págs. 1-64
• Idioma: inglés
• Enlaces
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• Resumen

  • 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.