Kato’s Euler system and rational points on elliptic curves I: A p-adic Beilinson formula
Kato’s Euler system and rational points on elliptic curves I: A p-adic Beilinson formula
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加藤欧拉系统和椭圆曲线上的有理点 I：p 进 Beilinson 公式
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
H. Darmon
中科院分区：
文献类型：
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作者：
M. Bertolini;H. Darmon
这篇文章是一系列致力于加藤的欧拉系统所产生的p-adic家庭的贝林森元素在K理论的模曲线。证明了一个p-adic Beilinson公式，它将模曲线K-理论中某些特殊元素的合成调节子（Coleman-de Shalit和Besser意义下）与权为2的尖点形式的Mazur-Swinnerton-Dyer p-adic L-函数在≥ 2的整数点处的特殊值联系起来.当结合显式的关系syntomic调节器和p-adic étale上同调，这导致了一个替代的证明的主要结果[Br 2]和[Ge]这是独立的加藤的显式互惠法。
This article is the first in a series devoted to Kato’s Euler system arising from p-adic families of Beilinson elements in the K-theory of modular curves. It proves a p-adic Beilinson formula relating the syntomic regulator (in the sense of Coleman-de Shalit and Besser) of certain distinguished elements in the K-theory of modular curves to the special values at integer points ≥ 2 of the Mazur-Swinnerton-Dyer p-adic L-function attached to cusp forms of weight 2. When combined with the explicit relation between syntomic regulators and p-adic étale cohomology, this leads to an alternate proof of the main results of [Br2] and [Ge] which is independent of Kato’s explicit reciprocity law.