Let L be a finite Galois CM-extension of a totally real field K. We show that the validity of an appropriate special case of the Equivariant Tamagawa Number Conjecture leads to a natural construction for each odd prime p of explicit elements in the (non-commutative) Fitting invariants over of a certain tame ray class group, and hence also in the analogous Fitting invariants of the p-primary part of the ideal class group of L. These elements involve the values at s=1 of the Artin L-series of characters of the group Gal(L/K). We also show that our results become unconditional under certain natural hypotheses on the extension L/K and prime p.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa160-1-5,
author = {Hugo Castillo and Andrew Jones},
title = {On the values of Artin L-series at s=1 and annihilation of class groups},
journal = {Acta Arithmetica},
volume = {161},
year = {2013},
pages = {67-93},
zbl = {06189627},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa160-1-5}
}
Hugo Castillo; Andrew Jones. On the values of Artin L-series at s=1 and annihilation of class groups. Acta Arithmetica, Tome 161 (2013) pp. 67-93. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa160-1-5/