13 problems

$C_{\mathrm{Iw}}(K_\infty/K,V)$. 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 $F$ be a totally real field in which $p$ is unramified, let $G_F$ be its absolute Galois group, and let $\Sigma_v$ denote the embeddings associated with a place $v\mid p$. Let…

Let $K$ be a complete discrete valuation field of mixed characteristic $(0,p)$ with perfect residue field $k$, and let $G_K=\operatorname{Gal}(\overline{K}/K)$. Fix a positive inte…

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 $p$…

Sun–Yang–Zuo conjecture.

Sun–Yang–Zuo conjecture. A Higgs bundle in $\mathcal M_\lambda$ over a finite unramified extension is twisted $f$-periodic if and only if $\pi^*(\theta_0)$ is a $(p^f\pm1)$-torsion…

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…

Let $r$ be a positive integer written as $r=t(p-1)+s$ with $t\geqslant 0$ and $s\in\{1,\ldots,p-1\}$, let $a\in\overline{\mathbb Q}_p$ with $v=v(a)\geqslant 1$, and define the risi…

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.