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Relative fundamental groups and rational points
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Lazda, Christopher (2015) Relative fundamental groups and rational points. The Rendiconti del Seminario Matematico della Università di Padova, 134 . pp. 1-45. doi:10.4171/RSMUP/134-1 ISSN 0041-8994.
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Official URL: https://doi.org/10.4171/RSMUP/134-1
Abstract
In this paper we define a relative rigid fundamental group, which associates to a section p of a smooth and proper morphism f:X→S in characteristic p, a Hopf algebra in the ind-category of overconvergent F-isocrystals on S. 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 f. 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.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Journal or Publication Title: | The Rendiconti del Seminario Matematico della Università di Padova | ||||||
Publisher: | C E D A M | ||||||
ISSN: | 0041-8994 | ||||||
Official Date: | 17 November 2015 | ||||||
Dates: |
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Volume: | 134 | ||||||
Page Range: | pp. 1-45 | ||||||
DOI: | 10.4171/RSMUP/134-1 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 14 October 2019 | ||||||
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