On the section conjecture over function fields and finitely generated fields
Saidi, Mohamed
Date: 14 November 2016
Article
Journal
Publications of the Research Institute for Mathematical Sciences
Publisher
European Mathematical Society
Publisher DOI
Abstract
We investigate sections of arithmetic fundamental groups of hyperbolic curves over function fields. As a consequence we prove that the anabelian section conjecture of Grothendieck holds over all finitely generated fields over Q if it holds over all number fields, under the condition of finiteness (of the -primary parts) of certain ...
We investigate sections of arithmetic fundamental groups of hyperbolic curves over function fields. As a consequence we prove that the anabelian section conjecture of Grothendieck holds over all finitely generated fields over Q if it holds over all number fields, under the condition of finiteness (of the -primary parts) of certain Shafarevich-Tate groups. We also prove that if the section conjecture holds over all number fields then it holds over all finitely generated fields for curves which are defined over a number field.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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