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arXiv · 2412.13812

On characteristic elements modulo $p$ in non-commutative Iwasawa theory

Meng Fai Lim·Chao Qin
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Abstract

Coates, Fukaya, Kato, Sujatha and Venjakob come up with a procedure of attaching suitable characteristic element to Selmer groups defined over a non-commutative $p$-adic Lie extension, which is subsequently refined by Burns and Venjakob. By their construction, these characteristic elements are realized as elements in an appropriate localized $K_1$-group. In this paper, we will introduce a notion of modulo $p$ for these elements and study some of their properties. As an application, we study the Greenberg Selmer group of a tensor product of modular forms, where $p$ is an Eisenstein prime for one of these forms.

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Meng Fai Lim, Chao Qin. 2024-12-18. On characteristic elements modulo $p$ in non-commutative Iwasawa theory. https://doi.org/10.4310/pamq.250324140937

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