10 problems

Let $(R,T,\zeta)$ be a triple as in the paper's setup, where $T$ is an $R$-representation of $G_{\mathbb Q_p}$ and $\zeta$ is a $\mathbb Z_p$-basis of…

Fukaya–Kato's local epsilon-isomorphism conjecture. For every such de Rham representation $V_\chi$, one has

Let $\Lambda$ be the Iwasawa algebra of the relevant $p$-adic Lie group, let $\widetilde\Lambda$ be its unramified coefficient extension, and let $\mathbb T$ be the associated big…

Nakayama's local epsilon conjecture. There exists an isomorphism

Nakayama's local epsilon conjecture. There exists a unique isomorphism

Let $T$ be $r$-critical and let $T(\chi)$ be $s$-critical with $r\ge s$. Suppose the local Panchishkin subrepresentations satisfy $T_v^{++}\subseteq T_v^+$, and let rank-lowering o…

Let $F_\infty/K$ be the $p$-adic Lie extension in the rank-lowering setup, let $\Lambda(\Gamma)$ be its Iwasawa algebra, and let $T_v^\sharp=T_v^+/T_v^{++}$ be the local quotient o…

Let $S$ be a finite set of places containing $p$, let $T$ be an $R$-representation of $G_{\mathbb{Q},S}$, and let $T^*$ denote its relevant dual. Let…

Let $R$ be a coefficient ring and let $D$ be an étale $(\varphi,\Gamma)$-module over $\mathcal{E}_R$, of rank $r_D$. The convolution pairing induces an alternating map … Using the…

Fix a prime $l$. For a coefficient ring $R$, an $R$-representation $T$ of $G_{\mathbb{Q}_l}$, and a $\mathbb{Z}_l$-basis $\zeta$ of…