Étale homotopy sections of algebraic varieties
<p>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 invari...
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| Format: | Thesis |
| Language: | English |
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2014
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| _version_ | 1797080125986045952 |
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| author | Haydon, J |
| author2 | Kim, M |
| author_facet | Kim, M Haydon, J |
| author_sort | Haydon, J |
| collection | OXFORD |
| description | <p>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.</p> <p>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.</p> |
| first_indexed | 2024-03-07T00:55:42Z |
| format | Thesis |
| id | oxford-uuid:88019ba2-a589-4179-ad7f-1eea234d284c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:55:42Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | oxford-uuid:88019ba2-a589-4179-ad7f-1eea234d284c2022-03-26T22:14:09ZÉtale homotopy sections of algebraic varietiesThesishttp://purl.org/coar/resource_type/c_db06uuid:88019ba2-a589-4179-ad7f-1eea234d284cGroup theory and generalizations (mathematics)Algebraic geometryNumber theoryAlgebraic topologyEnglishOxford University Research Archive - Valet2014Haydon, JKim, M<p>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.</p> <p>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.</p> |
| spellingShingle | Group theory and generalizations (mathematics) Algebraic geometry Number theory Algebraic topology Haydon, J Étale homotopy sections of algebraic varieties |
| title | Étale homotopy sections of algebraic varieties |
| title_full | Étale homotopy sections of algebraic varieties |
| title_fullStr | Étale homotopy sections of algebraic varieties |
| title_full_unstemmed | Étale homotopy sections of algebraic varieties |
| title_short | Étale homotopy sections of algebraic varieties |
| title_sort | etale homotopy sections of algebraic varieties |
| topic | Group theory and generalizations (mathematics) Algebraic geometry Number theory Algebraic topology |
| work_keys_str_mv | AT haydonj etalehomotopysectionsofalgebraicvarieties |