The monodromy groups of lisse sheaves and overconvergent F-isocrystals

• Marco D'Addezio ^[1]
  1. [1] Max Planck Institute for Mathematics

     Max Planck Institute for Mathematics

     Kreisfreie Stadt Bonn, Alemania

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 3, 2020
• Idioma: inglés
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• Resumen

  • It has been proven by Serre, Larsen–Pink and Chin, that over a smooth curve over a finite field, the monodromy groups of compatible semi-simple pure lisse sheaves have “the same” π0 and neutral component. We generalize their results to compatible systems of semi-simple lisse sheaves and overconvergent F-isocrystals over arbitrary smooth varieties. For this purpose, we extend the theorem of Serre and Chin on Frobenius tori to overconvergent F-isocrystals. To put our results into perspective, we briefly survey recent developments of the theory of lisse sheaves and overconvergent F-isocrystals. We use the Tannakian formalism to make explicit the similarities between the two types of coefficient objects.