Perfect forms and the Vandiver conjecture

Details Perfect forms and the Vandiver conjecture Perfect forms and the Vandiver conjecture

1998-12-22

arxiv.org/abs/math/9812171v1

Mathematics

Number Theory

Scientific paper

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.

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