Points in algebraic geometry

• Ofer Gabber ^[1] ; Shane Kelly ^[2]
  1. [1] Institut des Hautes Études Scientifiques

     Institut des Hautes Études Scientifiques

     Arrondissement de Palaiseau, Francia

     
  2. [2] Tokyo Institute of Technology

     Tokyo Institute of Technology

     Japón

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 10 (October 2015), 2015, págs. 4667-4680
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2015.03.001
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• Resumen

  • We give scheme-theoretic descriptions of the category of fibre functors on the categories of sheaves associated to the Zariski, Nisnevich, étale, rh, cdh, ldh, eh, qfh, and h topologies on the category of separated schemes of finite type over a separated noetherian base. Combined with a theorem of Deligne on the existence of enough points, this provides an algebro-geometric description of a conservative family of fibre functors on these categories of sheaves. As an example of an application we show that direct image along a closed immersion is exact for all these topologies except qfh. The methods are transportable to other categories of sheaves as well.