Giordano Favi, Mathieu Florence: Tori and essential dimension

giordano.favi@gmail.com, mathieu.florence@gmail.com

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.

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