Stratified bundles and étale fundamental group

• Hélène Esnault ^[2] ; Xiaotao Sun ^[1]
  1. [1] Chinese Academy of Science and Technology for Development

     Chinese Academy of Science and Technology for Development

     China

     
  2. [2] Freie Universität Berlin, Germany
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 13, Nº 3, 2014, págs. 795-812
• Idioma: inglés
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• Resumen

  • For a smooth projective variety X over an algebraically closed field of characteristic p > 0, we show that all irreducible stratified bundles on X have rank 1 if and only if the commutator [⇡1, ⇡1] of the ´etale fundamental group ⇡1 of X is a pro-p-group, and we prove that the category of stratified bundles is semi-simple with irreducible objects of rank 1 if and only if ⇡1 is Abelian without p-power quotient. This answers positively a conjecture by Gieseker [4, page 8].