Sharifi猜想中的层次兼容性

Pub Date : 2022-08-14 DOI:10.4153/s0008439523000267
E. Lecouturier, Jun Wang
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引用次数: 1

摘要

Sharifi构造了从模曲线$X_1(M)$到$K$群$K_2(\mathbf{Z}[\zeta_M,\frac{1}{M}])$的第一同源性的映射,其中$\zeta_M$是单位的原始$M$根。我们研究了当$M$变化时,这些地图是如何关联的。我们的方法依赖于Sharifi和Venkatesh开发的技术。
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Level compatibility in Sharifi’s conjecture
Sharifi has constructed a map from the first homology of the modular curve $X_1(M)$ to the $K$-group $K_2(\mathbf{Z}[\zeta_M, \frac{1}{M}])$, where $\zeta_M$ is a primitive $M$th root of unity. We study how these maps relate when $M$ varies. Our method relies on the techniques developed by Sharifi and Venkatesh.
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