15 problems

Let $\mathcal{K}$ be a finite extension of $\mathbb{Q}_p$, let $\mathcal{O}$ be its valuation ring, and let $\mathbf{A}(\rho)=\mathbf{V}_\rho/\mathbf{T}_\rho$ be the $p$-divisible mod…

Coates–Sujatha's conjecture. For every elliptic curve $E$ over a number field $K$, $Y(E/\textbf{K})$ is a finitely generated $\mathbb{Z}_p$-module.

Let $F$ be a number field, let $p$ be an odd prime, and let $F_\text{cyc}$ be the cyclotomic $\mathbb{Z}_p$-extension of $F$. For an elliptic curve $E$ over $F$, write…

Coates–Sujatha's pseudo-nullity conjecture. The module

Let $p$ be a prime number, let $F$ be a number field, let $\mathcal{O}$ be the ring of integers of a finite extension of $\mathbb{Q}_p$, and let $S$ be a finite set of primes of…

Let $K$ be the function field considered in the paper, let $L$ be a finite extension of $K$, and let $L_\mathrm{cyc}$ be its cyclotomic extension. For an elliptic curve $E/L$, let…

Let $E/\mathbb{Q}$ be an elliptic curve, let $p$ be a prime of good reduction, and let $\mathcal{R}_{p^\infty}(E/\mathbb{Q}_{\operatorname{cyc}})$ be the fine Selmer group over the…

Let $\bar{A}$ be one of the coefficient objects considered in the source, with coefficient ring $\bar{R}$, and let $F_\infty/F$ be a $p$-adic Lie extension such that…

Retain the Hida-family settings of the source. Let $\mathcal{A}$ be the big Galois representation, let $F_\infty$ be a $\mathbb{Z}_{p}$-extension of a number field $F$, and write…

Let $L_\infty$ be a $\mathbb{Z}_{p}^{2}$-extension of a number field $F$ containing the cyclotomic $\mathbb{Z}_{p}$-extension $F^{\mathrm{cyc}}$. Let…

Let $f$ be a normalized cuspidal eigenform as in the source, let $A_f$ be the associated discrete Galois representation, and let $F_\infty$ be a $\mathbb{Z}_{p}$-extension of a num…

Let $K$ be a number field, let $p$ be a prime, let $M$ be a representation of $\operatorname{G}_K$ on a finite-dimensional vector space over $\mathbb{F}_p$, and let $S$ contain the…

Let $K$ be a number field, let $p$ be a prime, and let $M$ be a representation of $\operatorname{G}_K$ on a finite-dimensional vector space over $\mathbb{F}_p$. For such a represen…

Let $l$ be an odd prime, let $F$ be an imaginary quadratic field, and let $\mathcal{E}$ be an elliptic curve over $F$. Let $F^{\mathrm{anti}}$ be the anticyclotomic $\mathbb{Z}_l$-…

Let $l$ be an odd prime, let $F$ be a number field, and let $\mathcal{E}$ be an elliptic curve over $F$. For an extension $L/F$ in the maximal extension unramified outside the pres…