10 problems

Let $K\subset\mathbb C_p$ be a discrete valuation subfield, meaning that its valuation is induced from the valuation on $\mathbb C_p$, and let $R$ be the valuation ring of $K$. Ass…

For an integer $n\geq 2$, let $R\Gamma(\mathbb{C}_p^\mathrm{Syn},\mathcal{O}\{n\})$ denote analytic syntomic cohomology of $\mathbb{C}_p$ with coefficients in the $n$-th Tate-twist…

Let $\bbS^{\widehat{\mathbbl{\Delta}}}$ be the complement of the zero section in the universal formal group $\widehat{\bbG}_\mathrm{univ}=\bbS^{\widehat{\calN}}$, regarded as an an…

Let $\bbS^\mathrm{Syn}$ be the syntomic stack, and let $\bbM_{\mathrm{m}\ifthenelse{\equal{\bbS}{}}{}{,\bbS}}^\mathrm{Syn}$ be the associated monoid stack. Consider the map from…

Let $\bbS^\mathrm{Syn}$ be the syntomic stack and let $\bbM_{\mathrm{m}\ifthenelse{\equal{\bbS}{}}{}{,\bbS}}^\mathrm{Syn}$ be its associated monoid stack. Let…

Perrin-Riou's conjecture. The special values of the $p$-adic $L$-functions are described by syntomic regulators up to ${\mathbb Q}^{\times}$.

Syntomic sheaf conjecture. The sheaf of complexes $\mathbb Z_p(i)$ on $\mathrm{QRSPerfd}$ is locally concentrated in degree $0$ and is given by a $p$-torsion-free sheaf. Equivalent…

Let $p$ be prime, let $K$ be a finite extension of $\mathbb{Q}_p$ with ring of integers $\mathcal{O}_K$, and let $\mathcal{X}$ be a smooth proper scheme over $\mathcal{O}_K$ with g…

Bes and de Jeu's syntomic regulator conjecture. This map is the composition

Let $F$ be the function field associated with the curve $C$, and let $\mathscr{C}$ denote the corresponding curve in place of the integral model $\mathcal{O}$. The preceding theore…