Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.711826
Title: Topics in the theory of Selmer varieties
Author: Dogra, Netan
ISNI:       0000 0004 6061 2711
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2015
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Abstract:
The Selmer varieties of a hyperbolic curve X over ℚ are refinements of the Selmer group arising from replacing the Tate module of the Jacobian with higher quotients of the unipotent étale fundamental group. It is hoped that these refinements carry extra arithmetic information. In particular the nonabelian Chabauty method developed by Kim uses the Selmer variety to give a new method to find the set X(ℚ). This thesis studies certain local and global properties of the Selmer varieties associated to finite dimensional quotients of the unipotent fundamental group of a curve over ℚ. We develop new methods to prove finiteness of the intersection of the Selmer varieties with the set of local points (and hence of the set of rational points) and new methods to implement this explicitly, giving the first examples of explicit nonabelian Chabauty theory for rational points on projective curves.
Supervisor: Kim, Minhyong Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.711826  DOI: Not available
Keywords: Mathematics--Study and teaching ; Arithmetic Fundamental Groups ; Number Theory ; Diophantine Geometry
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