Nori fundamental gerbe of essentially finite covers and Galois closure of towers of torsors

• Marco Antei ^[1] ; Indranil Biswas ^[4] ; Michel Emsalem ^[5] ; Fabio Tonini ^[2] ; Lei Zhang ^[3]
  1. [1] Universidad de Costa Rica

     Universidad de Costa Rica

     Hospital, Costa Rica

     
  2. [2] University of Florence

     University of Florence

     Firenze, Italia

     
  3. [3] Chinese University of Hong Kong

     Chinese University of Hong Kong

     RAE de Hong Kong (China)

     
  4. [4] Tata Institute of Fundamental Research, India
  5. [5] Université des Sciences et des Technologies de Lille 1, Francia

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 25, Nº. 2, 2019
• Idioma: inglés
• DOI: 10.1007/s00029-019-0449-z
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• Resumen

  • We prove the existence of a Galois closure for towers of torsors under finite group schemes over a proper, geometrically connected and geometrically reduced algebraic stack X over a field k. This is done by describing the Nori fundamental gerbe of an essentially finite cover of X. A similar result is also obtained for the S -fundamental gerbe.