Incompressibility of Generic Torsors of Norm Tori.

Let p be a prime integer, F a field of characteristic not p, T the norm torus of a degree p extension field of F, and E a T-torsor over F such that the degree of each closed point on E is divisible by p (a generic T-torsor has this property). We prove that E is p-incompressible. Moreover, all smooth compactifications of E (including those given by toric varieties) are p-incompressible. The main requisites of the proof are: (1) A. Merkurjev's degree formula (requiring the characteristic assumption), generalizing M. Rost's degree formula, and (2) combinatorial construction of a smooth projective fan invariant under an action of a finite group on the ambient lattice due to J.-L. Colliot- Thélène-D. Harari-A. N. Skorobogatov, produced by refinement of J.-L. Brylinski's method with the help of an idea of K. Künnemann. [ABSTRACT FROM AUTHOR]