9 problems

Let $G\,|\,V$ be a polar representation, let $f:V\to Q$ be the quotient map, and set … An $A_f$ stratification is the stratification condition described in Section 2.2.1. The Af st…

Loeser's generalized monodromy conjecture. For almost all finite places $\mathfrak P$, if $H$ is a polar hyperplane in $\mathcal P(Z_\phi(F_{\mathfrak P},\chi;s))$, with $\phi$ res…

Gabber–Abe conjecture. If $(f,K)$ is Ψ-good, then $(f,R(\Psi_f)_u^tK)$ is Ψ-good and $(f,K)$ is Ψ-factorizable.

Let $K$ be a local field with residue characteristic $p$, let $\ell\neq p$ be a prime number, and let $\mathcal X$ be an admissible formal $\mathcal O_K$-scheme with smooth generic…

Let $C\rightsquigarrow C_0$ be a degeneration of a smooth complex projective curve to a nodal curve, with marked points $S\rightsquigarrow S_0$ disjoint from the nodes. Let…

Let $S$ be a strictly henselian trait with algebraically closed residue field, and let $X$, $x$, $\mathcal F$, and $\mathcal F'$ be as in Theorem: $X$ is a strictly local $S$-schem…

Test function conjecture. As elements of $\mathcal Z(G(E_0),\mathcal G(\mathcal O_{E_0}))$,

Let $\mathcal{Z}^{\vee}\in\textbf{DM}_{\text{gm}}(\mathbb{Q},\mathbb{Q})$ be the dual limit mixed motive, and let $\mathbf{Z}^{\bullet}$ be the complex in…

Let $Sh_{K_p}$ be the Shimura variety, let $\mathcal M_{K_p}/\mathcal O_E$ be a natural integral model, and let $R\Psi_x$ denote the nearby-cycles complex at a point $x$ of its spe…