The lifted root number conjecture for fields of prime degree over the rationals: an approach via trees and Euler systems

Greither, Cornelius, and Kučera, Radiu. "The lifted root number conjecture for fields of prime degree over the rationals: an approach via trees and Euler systems." Annales de l’institut Fourier 52.3 (2002): 735-777. <http://eudml.org/doc/115993>.

@article{Greither2002,
abstract = {The so-called Lifted Root Number Conjecture is a strengthening of Chinburg’s $\Omega (3)$- conjecture for Galois extensions $K/F$ of number fields. It is certainly more difficult than the $\Omega (3)$-localization. Following the lead of Ritter and Weiss, we prove the Lifted Root Number Conjecture for the case that $F=\{\mathbb \{Q\}\}$ and the degree of $K/F$ is an odd prime, with another small restriction on ramification. The very explicit calculations with cyclotomic units use trees and some classical combinatorics for bookkeeping. An important point is the following: While dealing with our Euler systems, we have to keep track of the action of the Galois group, whose order is not invertible in the coefficient ring $\{\mathbb \{Z\}\}_p$. At the end we prove a generalization of the well-known Rédei-Reichardt theorem and explain the close link with our theory.},
affiliation = {Universität des Bundeswehr München, Fakultät fur Informatik, Institut für theoretische Informatik und Mathematik, 85577 Neubiberg (Allemagne); Masarykova Univerzita, P\{ř\}íprodov\{ě\}decká Fakulta, Janá\{č\}kovo nám 2a, 663 95 Brno (République Tchèque)},
author = {Greither, Cornelius, Kučera, Radiu},
journal = {Annales de l’institut Fourier},
keywords = {lifted Chinburg conjecture; Euler systems; combinatorics; trees},
language = {eng},
number = {3},
pages = {735-777},
publisher = {Association des Annales de l'Institut Fourier},
title = {The lifted root number conjecture for fields of prime degree over the rationals: an approach via trees and Euler systems},
url = {http://eudml.org/doc/115993},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Greither, Cornelius
AU - Kučera, Radiu
TI - The lifted root number conjecture for fields of prime degree over the rationals: an approach via trees and Euler systems
JO - Annales de l’institut Fourier
PY - 2002
PB - Association des Annales de l'Institut Fourier
VL - 52
IS - 3
SP - 735
EP - 777
AB - The so-called Lifted Root Number Conjecture is a strengthening of Chinburg’s $\Omega (3)$- conjecture for Galois extensions $K/F$ of number fields. It is certainly more difficult than the $\Omega (3)$-localization. Following the lead of Ritter and Weiss, we prove the Lifted Root Number Conjecture for the case that $F={\mathbb {Q}}$ and the degree of $K/F$ is an odd prime, with another small restriction on ramification. The very explicit calculations with cyclotomic units use trees and some classical combinatorics for bookkeeping. An important point is the following: While dealing with our Euler systems, we have to keep track of the action of the Galois group, whose order is not invertible in the coefficient ring ${\mathbb {Z}}_p$. At the end we prove a generalization of the well-known Rédei-Reichardt theorem and explain the close link with our theory.
LA - eng
KW - lifted Chinburg conjecture; Euler systems; combinatorics; trees
UR - http://eudml.org/doc/115993
ER -