Patching subfields of division algebras
Patching subfields of division algebras
复制标题
修补除法代数的子域
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
D. Krashen
中科院分区：
文献类型：
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作者：
D. Harbater;Julia Hartmann;D. Krashen
给定一个域 F，人们可能会问哪些有限群是域扩展 E/F 的伽罗瓦群，使得 E 是中心为 F 的除代数的最大子域。这个问题最初由 Schacher 提出，他给出了有理数域的部分结果。使用修补，我们在 F 是具有特征零的代数闭残差域的完整离散值域上的曲线的函数域的情况下给出了此类群的完整表征，以及相关情况下的结果。
Given a field F, one may ask which finite groups are Galois groups of field extensions E/F such that E is a maximal subfield of a division algebra with center F. This question was originally posed by Schacher, who gave partial results over the field of rational numbers. Using patching, we give a complete characterization of such groups in the case that F is the function field of a curve over a complete discretely valued field with algebraically closed residue field of characteristic zero, as well as results in related cases.