Computation of some essential dimensions

by Markus Rost (Preprint, August 2000, December 2008, 19 pages)

In these notes we show that the essential dimension of PGL₄ is equal to 5.

Along the way we discuss (in a rather unsystematic manner) generalities on essential dimension and degree formulas.

Full text (version of December 13, 2008): [dvi] [dvi.gz] [pdf] [ps] [ps.gz]

Update December 2008:

There was a gap in the proof of Lemma 11.3, which is hopefully now fixed.
There is the preprint "Essential p-dimension of PGL(p^2)" by A. Merkurjev (November 2008).

Essential dimension of twisted C₄

by Markus Rost (Notes, March 2002, 3 pages)

In this note we compute the essential dimension of a Galois module which is cyclic of order 4 (in characteristic different from 2).

Full text (version of March 2, 2002): [dvi] [dvi.gz] [pdf] [pdf.gz] [ps] [ps.gz]