On the values of Artin L-series at s=1 and annihilation of class groups

Hugo Castillo, and Andrew Jones. "On the values of Artin L-series at s=1 and annihilation of class groups." Acta Arithmetica 160.1 (2013): 67-93. <http://eudml.org/doc/279125>.

@article{HugoCastillo2013,
abstract = {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 $ℤ_p[G]$ 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.},
author = {Hugo Castillo, Andrew Jones},
journal = {Acta Arithmetica},
keywords = {Artin L-series; p-adic regulators; Tamagawa number conjectures; class groups},
language = {eng},
number = {1},
pages = {67-93},
title = {On the values of Artin L-series at s=1 and annihilation of class groups},
url = {http://eudml.org/doc/279125},
volume = {160},
year = {2013},
}

TY - JOUR
AU - Hugo Castillo
AU - Andrew Jones
TI - On the values of Artin L-series at s=1 and annihilation of class groups
JO - Acta Arithmetica
PY - 2013
VL - 160
IS - 1
SP - 67
EP - 93
AB - 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 $ℤ_p[G]$ 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.
LA - eng
KW - Artin L-series; p-adic regulators; Tamagawa number conjectures; class groups
UR - http://eudml.org/doc/279125
ER -