18 problems

Let $H_g$ be the number field cut out by the Artin representation attached to the adjoint of $g$, and let $H_{g,p}$ be a completion of $H_g$ at a prime above $p$. Let…

Fontaine–Perrin-Riou's conjecture. The category

The twisted exceptional zero conjecture. For every such $\chi$,

Let $E/\mathbb{Q}$ have split multiplicative reduction at a prime $p$, put $G_p=\left(\mathbb{Z}/p\mathbb{Z}\right)^*/\langle-1\rangle$, and let $\lambda(a,p)$ be the even modular…

Kummer-motive p-adic period conjecture. The transcendence degree of the $p$-adic periods of $K_a^\vee$ is $1$; equivalently, $\frac{\log(a^{1-p})}{1-p}$ is transcendental.

André's conjecture. The phenomenon in which the Betti and de Rham $\overline{\mathbb Q}$-structures coincide should be pathological.

Weak p-adic Grothendieck period conjecture. The inclusion

Homogeneous-space p-adic Grothendieck period conjecture. The variety $\mathcal H_M$ is irreducible and

Motivic p-adic Grothendieck period conjecture. The affine scheme

Ayoub's conjecture. This algebra should be the algebra of functions on a homogeneous motivic space, but not on a motivic torsor.

Tensorial p-adic Grothendieck period conjecture. The inequality

Let $H$ be the number field cut out by $V_{gh}$, let $L$ be a finite extension of $\mathbb Q$ containing the relevant Fourier coefficients and Hecke roots, and let…

The p-adic period conjecture. For every open integer scheme $Z$, the period map $\operatorname{per}_{\pf}\colon A(Z)\to\mathbb{Q}_p$ is injective. This is presented as a $p$-adic a…

For an open subscheme $Z\subset\operatorname{Spec}\mathbb{Z}$ and a prime $p\in Z$, the $p$-adic zeta values $\zeta^p(n)$ are known to be nonzero when $n$ is odd and $n\geq 3$ and…

Let $\mathcal{MT}(\mathbb{Z})$ be the category of mixed Tate motives over $\mathbb{Z}$, let $\mathcal{P}^{\mathfrak{dr}}$ be its de Rham period algebra, and let … be the $p$-adic p…

Period conjecture. For every integer $n$,

Let $\cH$ be the ring of motivic multiple zeta values, with period map $per:\cH\to\mathbb{R}$, and let $\cA:=\cH/\zeta^{\fm}(2)\cH$. For each prime $p$, the induced $p$-adic period…

Let $p\geq 5$ be a prime, let $K$ be the quadratic unramified extension of $\mathbf{Q}_p$, and let $X_0(p)_K$ be the modular curve with associated rigid curve uniformized as…