Relative fundamental groups and rational points

  • Christopher Lazda

    Imperial College, London, UK

Abstract

In this paper we define a relative rigid fundamental group, which associates to a section pp of a smooth and proper morphism f:XSf:X\rightarrow S in characteristic pp, a Hopf algebra in the ind-category of overconvergent FF-isocrystals on SS. We prove a base change property, which says that the fibres of this object are the Hopf algebras of the rigid fundamental groups of the fibres of ff. We explain how to use this theory to define period maps as Kim does for varieties over number fields, and show in certain cases that the targets of these maps can be interpreted as varieties.

Cite this article

Christopher Lazda, Relative fundamental groups and rational points . Rend. Sem. Mat. Univ. Padova 134 (2015), pp. 1–45

DOI 10.4171/RSMUP/134-1