A Valuation Theoretic Approach to Essential Dimension

Details A Valuation Theoretic Approach to Essential Dimension A Valuation Theoretic Approach to Essential Dimension

2012-02-24

arxiv.org/abs/1202.5363v1

Mathematics

Algebraic Geometry

This is a Master's thesis at the University of British Columbia, Vancouver, December 2006

Scientific paper

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.

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