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Notes on the module of Euler systems for $p$-adic representations

Volume 205 / 2022

Ryotaro Sakamoto Acta Arithmetica 205 (2022), 137-160 MSC: Primary 11R23; Secondary 11R34. DOI: 10.4064/aa211024-13-6 Published online: 19 September 2022


We study the module of Euler systems for $p$-adic representations. We determine the ideal of an Iwasawa algebra associated with Euler systems of rank $0$. We also show that the module of higher rank Euler systems for $\mathbb G_{\mathrm m}$ over a totally real field is free of rank 1 under the assumptions that Greenberg’s conjecture holds true and that the $\mu $-invariant of a certain Iwasawa module vanishes.


  • Ryotaro SakamotoDepartment of Mathematics
    University of Tsukuba
    1-1-1 Tennodai
    Tsukuba, Ibaraki 305-8571, Japan

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