Quelques classes caracteristiques en theorie des nombres
Number Theory
2009-10-31 v1 K-Theory and Homology
Abstract
Let A be an arbitrary ring. We introduce a Dennis trace map mod n, from K_1(A;Z/n) to the Hochschild homology group with coefficients HH_1(A;Z/n). If A is the ring of integers in a number field, explicit elements of K_1(A,Z/n) are constructed and the values of their Dennis trace mod n are computed. If F is a quadratic field, we obtain this way non trivial elements of the ideal class group of A. If F is a cyclotomic field, this trace is closely related to Kummer logarithmic derivatives; this trace leads to an unexpected relationship between the first case of Fermat last theorem, K-theory and the number of roots of Mirimanoff polynomials.
Cite
@article{arxiv.math/0006237,
title = {Quelques classes caracteristiques en theorie des nombres},
author = {Max Karoubi and Thierry Lambre},
journal= {arXiv preprint arXiv:math/0006237},
year = {2009}
}