椭圆曲线在-扩展中的shafarevic - tate群的秩跳和增长

Pub Date : 2023-05-29 DOI:10.1017/s1446788723000034

Lea Beneish, Debanjana Kundu, Anwesh Ray

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引用次数: 1

摘要

设p为质数。本文利用Iwasawa理论的方法研究了椭圆曲线在p次循环扩展中的秩跳问题，并研究了p-初生Selmer群和shafareich - tate群在p次循环扩展中的生长，在此方向上对已有的结果进行了改进。

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RANK JUMPS AND GROWTH OF SHAFAREVICH–TATE GROUPS FOR ELLIPTIC CURVES IN -EXTENSIONS

Let p be a prime. In this paper, we use techniques from Iwasawa theory to study questions about rank jump of elliptic curves in cyclic extensions of degree p. We also study growth of the p-primary Selmer group and the Shafarevich–Tate group in cyclic degree-p extensions and improve upon previously known results in this direction.

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