karpenko at math.jussieu.fr

Submission: 2012, Aug 8

Let p be a prime integer, F a field of characteristic not p,
T the norm torus of a degree p^{n} 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^{n}
(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
a help of an idea of K. Künnemann.

2010 Mathematics Subject Classification: 14L17; 14C25

Keywords and Phrases: Algebraic tori, toric varieties, incompressibility, Chow groups and Steenrod operations.

Full text: dvi.gz 14 k, dvi 29 k, ps.gz 784 k, pdf.gz 100 k, pdf 124 k.

Server Home Page