Giordano Favi, Mathieu Florence: Tori and essential dimension,

Submission: 2006, Mar 2

The present paper deals with algebraic tori and essential dimension but in three unrelated contexts. After a recollection on essential dimension and generic torsors we explicitly construct a generic torsor for $\PGL_n$, $n$ odd. We also discuss the so called ``tori method" which gives a geometric proof of a result of Ledet on the essential dimension of a cyclic group (see \cite{JLY,Ledet}). In the last section we compute the essential dimension of the functor $K\mapsto H^1(K,\GL_n(\Z))$ that is the isomorphism classes of $n$-dimensional $K$-tori.

2000 Mathematics Subject Classification: 11E72, 16K20

Keywords and Phrases: Essential dimension, tori, generic torsors.

Full text: dvi.gz 27 k, dvi 62 k, ps.gz 754 k, pdf.gz 131 k, pdf 164 k.

Server Home Page