Thesis

### Étale homotopy sections of algebraic varieties

Abstract:

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”...

### Authors

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Merton College
Role:
Author

#### Contributors

Division:
MPLS
Department:
Mathematical Institute
Role:
Supervisor
Publication date:
2014
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
Oxford University, UK
Language:
English
Keywords:
Subjects:
UUID:
Local pid:
ora:8772
Deposit date:
2014-07-11