9 problems

Let $K/{\mathbb Q}_p$ be unramified, let $\overline\rho$ be absolutely irreducible, let $\lambda=(0,0)$ for each embedding, and let $t$ be a tame inertial type of level $f$. Let…

Let $K$ be a finite extension of $\Q_p$ with $p>2$, let $\mathbb F$ be a finite field, and let … be an $n$-dimensional continuous representation of the absolute Galois group…

Let $S$ be the set of indices at which the projection of the Kisin variety to the corresponding factor of $(\mathbb P^1_{k_E})^f$ is constant, and write $0=i_1<i_2<\cdots<i_r$ for…

Let $D^\psi({\bf v},{\rm t},\overline\rho)$ denote the potentially Barsotti–Tate deformation space, and let $\overline{\mathscr{G\!R}}^\psi({\bf v},{\rm t},\overline\rho)$ be the a…

Let $F$ be an unramified extension of ${\mathbb Q}_p$ of degree $f$, let ${\bf v}=(0,1)$, let ${\rm t}$ be a non-degenerate Galois type, and let…

Let $G$ be a connected reductive group over $k$, let $T$ be a maximal torus, let $W$ be its Weyl group, and fix a Weyl chamber. Let $\vec\rho$ be half the sum of the positive roots…

Weyl-group dimension conjecture. There exist constants $b_0$ and $c_0$ such that, for every $b\geqslant b_0$ and every dominant coweight $\mu$,

Motivic rationality conjecture. There exist polynomials $P,Q\in K_0(\operatorname{Var}_k)[X_1,\ldots,X_d]$ such that $Q(0,\ldots,0)$ is invertible in…

Let $M$ be the $d$-dimensional space equipped with an arbitrary $sigma$-semilinear operator $\sigma_M$, and let $\mathcal{X}_{\leqslant e}(\sigma_M)$, $\mathcal{X}_{\mu}(\sigma_M)$…