### Perfect forms and the Vandiver conjecture, by Christophe Soul'e

Let p be an odd prime, n an odd positive integer and C the p-Sylow subgroup
the class group of the p-cyclotomic extension of the rationals. When log(p)
is bigger than n**(224n**4), we prove that the eigenspace on C attached to
the (p-n)-th power of the Teichmuller character is trivial. The proof uses
the K-theory of the integers and the Voronoi reduction theory of quadratic
forms.

Christophe Soul'e <soule@ihes.fr>