English

Perfect forms and the Vandiver conjecture

Number Theory 2007-05-23 v1

Abstract

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.

Keywords

Cite

@article{arxiv.math/9812171,
  title  = {Perfect forms and the Vandiver conjecture},
  author = {Christophe Soulé},
  journal= {arXiv preprint arXiv:math/9812171},
  year   = {2007}
}