On the Preservation of Root Numbers and the Behavior of Weil Characters Under Reciprocity Equivalence

Canadian mathematical bulletin

关键词: $D$-space;    neighborhood assignment;    resolution;    boundary;   

DOI  :  10.4153/CMB-1997-048-2

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

This paper studies how the local root numbers and the Weil additivecharacters of the Witt ring of a number field behave underreciprocity equivalence. Given a reciprocity equivalence betweentwo fields, at each place we define a local square class whichvanishes if and only if the local root numbers are preserved. Thusthis local square class serves as a local obstruction to thepreservation of local root numbers. We establish a set ofnecessary and sufficient conditions for a selection of local squareclasses (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 classescombine to give a global square class which serves as a globalobstruction to the preservation of all root numbers. Lastly, weuse these results to study the behavior of Weil characters under reciprocity equivalence.

【 授权许可】

Unknown