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Title: Étale homotopy sections of algebraic varieties
Author: Haydon, James Henri
ISNI:       0000 0004 5354 102X
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2014
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We define and study the fundamental pro-finite 2-groupoid of varieties X defined over a field k. This is a higher algebraic invariant of a scheme X, analogous to the higher fundamental path 2-groupoids as defined for topological spaces. This invariant is related to previously defined invariants, for example the absolute Galois group of a field, and Grothendieck’s étale fundamental group. The special case of Brauer-Severi varieties is considered, in which case a “sections conjecture” type theorem is proved. It is shown that a Brauer-Severi variety X has a rational point if and only if its étale fundamental 2-groupoid has a special sort of section.
Supervisor: Kim, Minhyong Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Algebraic geometry ; Algebraic topology ; Group theory and generalizations (mathematics) ; Number theory ; higher-category theory ; homotopy theory ; arithmetic geometry