13 problems

Let $p$ be an odd prime, let $k\geqslant 2$ be an integer, and let $a\in\overline{\mathbb{Z}}_p$ satisfy $v_p(a)>0$. Let $V_{k,a}$ be the associated two-dimensional crystalline $p$…

$C_{\mathrm{Iw}}(K_\infty/K,V)$. The canonical trivialization satisfies

Let $V$ be a crystalline representation of $G_\ell$ over $K_\lambda$, and let $T\subseteq V$ be a $G_\ell$-stable $\mathcal{O}_\lambda$-lattice. Let $\omega$ and $\omega^*$ be latt…

Let $K$ be the finite unramified extension of $\mathbb Q_p$ used in the paper, let $G_K$ be its absolute Galois group, and let $\Sigma$ be the corresponding set of embeddings. Let…

Let $V$ be irreducible, crystalline, Frobenius semisimple with distinct Hodge–Tate weights $0$ and $k-1$. Let $\breve{\alpha}$ and $\breve{\beta}$ be the relevant Frobenius eigenva…

Sun–Yang–Zuo conjecture.

Let $p$ be a prime, let $f\in S_k(N)$ be a normalized eigenform of half-integral slope $\alpha$ with $0<\alpha\leqslant \frac{p-1}{2}$, and call $k$ exceptional for slope $\alpha$…

Let $\mathbb{F}$ be a finite field of characteristic $p$, let $K$ be a finite extension of $\mathbb{Q}_p$ with absolute Galois group $G_K$, and let $V_{\mathbb{F}}$ be an absolutel…

Crystalline lifts conjecture. Every mod $p$ residual representation admits a crystalline lift with non-positive Hodge–Tate weights.

Fix an $F$-crystalline representation $V$ of $G$ and a uniformizer $\pi \in K$. For each choice of a power series $f(u)$, let the associated Kisin module of $V$ be defined as in th…

Let $K/{\mathbb{Q}}_p$ be a finite totally ramified extension, and let ${\overline{\rho}}:G_K\to\operatorname{GL}_2({\overline{{\mathbb{F}}}_p})$ be a continuous representation. Le…

Let $\mathscr{S}_*^{\mathrm{cris}}$ denote the crystalline parameter space used in the paper. For $s\in\mathscr{S}_*^{\mathrm{cris}}$ non-exceptional, let…

Conjecture sur les points cristallins. Toute composante irréductible de ${\mathfrak X}_d$ contient un point cristallin absolument irréductible.