D -modules and finite monodromy

• Hélène Esnault ^[2] ; Mark Kisin ^[1]
  1. [1] Harvard University

     Harvard University

     City of Cambridge, Estados Unidos

     
  2. [2] Freie Universität Berlin
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 1, 2018, págs. 145-155
• Idioma: inglés
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• Resumen

  • We investigate an analogue of the Grothendieck p-curvature conjecture, where the vanishing of the p-curvature is replaced by the stronger condition, that the module with connection mod p underlies a DX-module structure. We show that this weaker conjecture holds in various situations, for example if the underlying vector bundle is finite in the sense of Nori, or if the connection underlies a Z-variation of Hodge structure. We also show isotriviality assuming a coprimality condition on certain mod p Tannakian fundamental groups, which in particular resolves in the projective case a conjecture of Matzat–van der Put.