论文标题
贝林森 - 卡托元素和$ p $ -adic $ l $ functions的插值
Interpolation of Beilinson-Kato elements and $p$-adic $L$-functions
论文作者
论文摘要
我们在本系列文章中的目标是本文是第一篇文章的第一篇文章，是在特征库上为Perrin-riou风格的构建（Bellaïche和Stevens）的$ p $ - 亚种$ l $ functions（Bellaïche和Stevens的）。作为第一种成分，我们在特征库（包括$θ$ - 批评点的社区）上插入了贝林森 - 卡托元素。一路上，我们证明了贝拉奇（Bellaïche）结果的典型变体，描述了特征库的局部特性。我们还开发了本地框架，以构建和建立这些$ p $ adic $ l $ functions的插值属性，而不是$θ$ - 批评点。
Our objective in this series of two articles, of which the present article is the first, is to give a Perrin-Riou-style construction of $p$-adic $L$-functions (of Bellaïche and Stevens) over the eigencurve. As the first ingredient, we interpolate the Beilinson-Kato elements over the eigencurve (including the neighborhoods of $θ$-critical points). Along the way, we prove étale variants of Bellaïche's results describing the local properties of the eigencurve. We also develop the local framework to construct and establish the interpolative properties of these $p$-adic $L$-functions away from $θ$-critical points.
