On the Preservation of Root Numbers and the Behavior of Weil Characters under Reciprocity Equivalence
Canadian mathematical bulletin, Tome 40 (1997) no. 4, pp. 402-415
Voir la notice de l'article provenant de la source Cambridge
This paper studies how the local root numbers and the Weil additive characters of the Witt ring of a number field behave under reciprocity equivalence. Given a reciprocity equivalence between two fields, at each place we define a local square class which vanishes if and only if the local root numbers are preserved. Thus this local square class serves as a local obstruction to the preservation of local root numbers. We establish a set of necessary and sufficient conditions for a selection of local square classes (one at each place) to represent a global square class. Then, given a reciprocity equivalence that has a finite wild set, we use these conditions to show that the local square classes combine to give a global square class which serves as a global obstruction to the preservation of all root numbers. Lastly, we use these results to study the behavior of Weil characters under reciprocity equivalence.
Carpenter, Jenna P. On the Preservation of Root Numbers and the Behavior of Weil Characters under Reciprocity Equivalence. Canadian mathematical bulletin, Tome 40 (1997) no. 4, pp. 402-415. doi: 10.4153/CMB-1997-048-2
@article{10_4153_CMB_1997_048_2,
author = {Carpenter, Jenna P.},
title = {On the {Preservation} of {Root} {Numbers} and the {Behavior} of {Weil} {Characters} under {Reciprocity} {Equivalence}},
journal = {Canadian mathematical bulletin},
pages = {402--415},
year = {1997},
volume = {40},
number = {4},
doi = {10.4153/CMB-1997-048-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1997-048-2/}
}
TY - JOUR AU - Carpenter, Jenna P. TI - On the Preservation of Root Numbers and the Behavior of Weil Characters under Reciprocity Equivalence JO - Canadian mathematical bulletin PY - 1997 SP - 402 EP - 415 VL - 40 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1997-048-2/ DO - 10.4153/CMB-1997-048-2 ID - 10_4153_CMB_1997_048_2 ER -
%0 Journal Article %A Carpenter, Jenna P. %T On the Preservation of Root Numbers and the Behavior of Weil Characters under Reciprocity Equivalence %J Canadian mathematical bulletin %D 1997 %P 402-415 %V 40 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1997-048-2/ %R 10.4153/CMB-1997-048-2 %F 10_4153_CMB_1997_048_2
Cité par Sources :