Euler方程组的Tamagawa亏损
Tamagawa defect of Euler systems
摘要：
正如在[Kolyvagin systems，by Barry Mazur and Karl Rubin]命题6.2.6和Buyukboduk[ arXiv：0706.0377v1 ]注释3.25中所指出的，如果p在不同于p的素数\ell处整除一个Tamagawa数，那么人们不期望从p进伽罗瓦表示T的欧拉系统得到的Kolyvagin系统是本原的（在[Kolyvagin systems，by Barry Mazur and Karl Rubin]定义4.5.5的意义上）;因此无法计算相关Selmer模的正确大小。本文利用T的Tamagawa数得到了Euler系统到Kolyvagin系统映射的上核大小的一个下界（参见[Kolyvagin systems，by Barry Mazur and Karl Rubin]的定理3.2.4），改进了[Kolyvagin systems，by Barry Mazur and Karl Rubin]的命题6.2.6.我们将展示如何这部分占失踪玉川因素加藤的计算与他的欧拉系统。
英文摘要：
As remarked in [Kolyvagin systems, by Barry Mazur and Karl Rubin] Proposition 6.2.6 and Buyukboduk[ arXiv:0706.0377v1 ] Remark 3.25 one does not expect the Kolyvagin system obtained from an Euler system for a p-adic Galois representation T to be primitive (in the sense of [Kolyvagin systems, by Barry Mazur and Karl Rubin] Definition 4.5.5) if p divides a Tamagawa number at a prime \ell different from p; thus fails to compute the correct size of the relevant Selmer module. In this paper we obtain a lower bound for the size of the cokernel of the Euler system to Kolyvagin system map (see Theorem 3.2.4 of [Kolyvagin systems, by Barry Mazur and Karl Rubin] for a definition of this map) in terms of the Tamagawa numbers of T, refining [Kolyvagin systems, by Barry Mazur and Karl Rubin] Propostion 6.2.6. We show how this partially accounts for the missing Tamagawa factors in Kato's calculations with his Euler system.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
