【摘 要】
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The Grunwald-Wang Theorem,a classical theorem in class field theory,was first formulated and claimed by W.Grunwald in 1933,and finally re-formulated and pro
【出 处】
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Algebraic geometry, number theory, and related topics(代数几何,数
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The Grunwald-Wang Theorem,a classical theorem in class field theory,was first formulated and claimed by W.Grunwald in 1933,and finally re-formulated and proved by Shiang-Hao Wang in 1950.It asserts that given a family of local multiplicative character ${ chi^{v},v in S}where chi^{v}: F_{v}^{ imes} o mathbb{C}^{ imes}$,there is a global multiplicative character χ of A × F whose order is minimal,and its local components at given places are given ones.In this talk,we will review this theorem,and also a proof of effective version,namely,not only we can prove the existence of such χ,but N(χ)can be bounded in an effective way.
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