Canadian mathematical bulletin | |
On the Preservation of Root Numbers and the Behavior of Weil Characters Under Reciprocity Equivalence | |
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
【 预 览 】
Files | Size | Format | View |
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RO201912050575960ZK.pdf | 36KB | download |