11 problems

Let $A$ be an abelian variety over a finite extension $F$ of $\mathbb Q$, let $p>2\dim(A)+1$ be prime, let $F_\infty=F(A_{p^\infty})$, and put…

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…

Assume that $A$ is an abelian variety over a number field $F$ with ordinary reduction at every prime above $p$, that $F_{\infty}$ is a uniform admissible $p$-adic extension of dime…

Let $A$ be an abelian variety over a number field $F$ with ordinary reduction at every prime above $p$, let $F_{\infty}$ be an admissible $p$-adic Lie extension containing…

Let $A$ be an abelian variety of dimension $g$ over a number field $F$, and let $F_{\infty}$ be a uniform admissible $p$-adic Lie extension containing $F^{\mathrm{cyc}}$. Put…

Let $M$ be an irreducible overconvergent $F$-isocrystal on $\operatorname{Spec}(F)$ with nonnegative slopes. Let $M^{u-r}$ be its unit-root subcrystal, and let $\eta$ be its first…

Let $p$ be a prime, let $F$ be a number field, and let $F_{\infty}$ be an $S$-admissible $p$-adic Lie extension of $F$. Let $R$ be a complete regular local ring with finite residue…

Let $F$ be a number field with no real primes when $p=2$, let $R$ be a complete regular local ring with finite residue field of characteristic $p$, let $T$ be a finite-rank free…

Let $E$ be an elliptic curve over $\mathbb Q$ with good supersingular reduction at $p$ and $a_p=0$. Let $L_\infty$ be a $p$-adic Lie extension of $\mathbb Q$ containing…

Let $E$ be an elliptic curve over $\mathbb Q$ with good supersingular reduction at $p$ and $a_p=0$. Let $L_\infty$ be a $p$-adic Lie extension of $\mathbb Q$ containing…

The $\mathfrak M_H(\Sigma)$-conjecture. If $p\geq 5$ and $E$ has good ordinary or split multiplicative reduction at all primes above $p$, then