Vanishing of Some Galois Cohomology Groups for Elliptic Curves
Vanishing of Some Galois Cohomology Groups for Elliptic Curves
复制标题
椭圆曲线的一些伽罗瓦上同调群的消失
DOI：
10.1007/978-3-319-45032-2_11
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
C. Wuthrich
中科院分区：
文献类型：
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作者：
T. Lawson;C. Wuthrich
设为椭圆曲线，p为素数，G为E上p-扭点的坐标与的扩张的Galois群。我们确定所有的情况下，伽罗瓦上同调群不消失，并调查类似的问题时。我们包括一个应用程序的验证某些情况下的伯奇和Swinnerton-Dyer猜想，和另一个应用程序的Grunwald-Wang问题的椭圆曲线。
Letbe an elliptic curve andpbe a prime number, and letGbe the Galois group of the extension ofobtained by adjoining the coordinates of thep-torsion points onE. We determine all cases when the Galois cohomology groupdoes not vanish, and investigate the analogous question forwhen. We include an application to the verification of certain cases of the Birch and Swinnerton-Dyer conjecture, and another application to the Grunwald–Wang problem for elliptic curves.