Notes on the module of Euler systems for $p$-adic representations
Volume 205 / 2022
Acta Arithmetica 205 (2022), 137-160
MSC: Primary 11R23; Secondary 11R34.
DOI: 10.4064/aa211024-13-6
Published online: 19 September 2022
Abstract
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.
