15 problems

Let $k_\infty/k$ be a $\mathds Z_p$-power extension with no finite place splitting completely, let $K_\infty=Kk_\infty$, and use the source's decomposition and character $\chi$ to…

Fix a subset $\Sigma\subseteq\Sigma_S(E)$ satisfying the source's condition, set $r=|\Sigma_S(\mathcal{K}_\infty)|$, $r'=|\Sigma|$, and…

Let $\mathcal{K}_\infty/K$ and $S$ be as in the source, put $\Sigma=\Sigma_S(\mathcal{K}_\infty)$ and $r=|\Sigma|$, and let $\Lambda(\mathcal{G}_\infty)$ be the relevant Iwasawa al…

Let $L/K$, $\Pi$, and $\Pi'$ be the fixed data, let $\Sigma$ be a subset of $\Sigma(L)$ with $\Sigma e Pi$, and let $p$ be a prime such that $O^\times{L, Pi, Pi',p}$ is torsion-fre…

Let $K_\infty/k$ be the relevant $mathds{Z}_p$-extension, let $\Gamma$ be its pro-$p$ direction, let $W=V'\setminus V$ have cardinality $e$, and let…

Let $K_\infty/k$ be the relevant $mathds{Z}_p$-extension with Galois group containing $\Gamma$, let $\Sigma$ and $T$ be the prescribed sets of places, and let $V'\setminus V=W$ hav…

Let $L_n/K$, $S$, and $\Sigma$ be as in the source, let $r_T$ be the specified rank, and let $\varepsilon_{L_n\mid K,S,\Sigma}$ be the $r_T$-th Rubin–Stark element. Let…

Let $S:=S_\infty(k)\cup S_p(k)\cup S_{\rm ram}(L/k)$, assume the Rubin–Stark conjecture for all finite subextensions of $Lk(p^\infty)/k$, and suppose that $p$ splits completely in…

Let $k_{\Gamma}/k$ be a $\mathbb{Z}_p$-extension with Galois group $\Gamma$, let $\Gamma_n:=\operatorname{Gal}(k_n/k)$, and put $L_\Gamma:=k_\Gamma L$. Let…

Mazur–Rubin–Sano conjecture. In the module

Iwasawa-theoretic Mazur–Rubin–Sano conjecture. There exists a unique

Local explicit Iwasawa main conjecture. For every height-one prime ideal $\mathfrak{p}$ of $\Lambda$,

Determinant-module Iwasawa main conjecture.

The p-component Rubin–Stark conjecture.

Let $\mathcal{S}^{E,p}_{\infty}$ be the cyclic $\Lambda$-module generated by the tower of Rubin–Stark elements after localization and twisting, let…