arXiv subjects

Aurel Meyer

Publications and source records attributed to Aurel Meyer.

6 recordsLinked to original sources

arXiv2012

A Valuation Theoretic Approach to Essential Dimension

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.

math.AG↗

arXiv2012

Essential p-dimension of algebraic groups whose connected component is a torus

Following up on our earlier work and the work of N. Karpenko and A. Merkurjev, we study the essential p-dimension of linear algebraic groups G whose connected component G^0 is a torus.

math.AG↗

arXiv2009

Essential p-dimension of algebraic tori

The essential dimension is a numerical invariant of an algebraic group G which may be thought of as a measure of complexity of G-torsors over fields. A recent theorem of N. Karpenko and A. Merkurjev gives a simple formula for the essential dimension of a finite p-group. We obtain similar formulas for the essential p-dimension of a broader class of groups, which includes all algebraic tori.

math.GR↗

arXiv2009

An upper bound on the essential dimension of a central simple algebra

We prove a new upper bound on the essential p-dimension of the projective linear group PGLn.

math.RA↗

arXiv2008

Some consequences of the Karpenko-Merkurjev theorem

We use a recent theorem of N. A. Karpenko and A. S. Merkurjev to settle several questions in the theory of essential dimension.

math.AG↗

arXiv2008

The essential dimension of the normalizer of a maximal torus in the projective linear group

Let p be a prime, k be a field of characteristic different from p containing a primitive p-th root of unity and N be the normalizer of the maximal torus in the projective linear group PGLn. We compute the exact value of the essential dimension ed(N;p) of N at p for every n.

math.AG↗