A Valuation Theoretic Approach to Essential Dimension
Algebraic Geometry
2012-02-27 v1
Abstract
In this essay we explore the notion of essential dimension using the theory of valuations of fields. Given a field extension K/k and a valuation on K that is trivial on k, we prove that the rank of the valuation cannot exceed the transcendence degree trdeg K. We use this inequality to prove lower bounds on the essential dimension in some interesting situations. We study orbits of a torus action and find a formula for the essential dimension of the functor of these orbits.
Keywords
Cite
@article{arxiv.1202.5363,
title = {A Valuation Theoretic Approach to Essential Dimension},
author = {Aurel Meyer},
journal= {arXiv preprint arXiv:1202.5363},
year = {2012}
}
Comments
This is a Master's thesis at the University of British Columbia, Vancouver, December 2006