9 problems

Let $f$ be a non-constant polynomial, and consider the Igusa local zeta function associated to $f$. A pole has maximal possible order if its order equals the largest order allowed…

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…

Igusa zeta function pole conjecture. The poles of the Igusa zeta function, after subtracting a natural number, are contained in the set of roots of $b_f(s)$.

The degree-five Igusa zeta function conjectures. The following two assertions are conjectured, with (b) stronger than (a): (a) $I_5(s)$ is a power series in $q$ and $t$ with positi…

Let $L$ be a non-Archimedean local field over $\operatorname{O}_K$, let $f\in\operatorname{O}_K[x_1,\ldots,x_n]$ be a nonconstant polynomial, let $\Phi$ be a Schwartz–Bruhat functi…

Let $f\in\operatorname{O}_K[x_1,\ldots,x_n]$ be a nonconstant polynomial, let $Z$ be a subscheme of $\mathbb A^n_{\operatorname{O}_K}$, and let $L$ be a non-Archimedean local field…

Let $f\in L[x_1,\dots,x_n]$ be a non-constant polynomial over a $p$-adic field $L$, let $\Phi$ be a Schwartz–Bruhat function on $L^n$, and consider the Igusa local zeta function wi…

Let $f$ be a polynomial and $Z$ a subvariety or closed subscheme around which the motivic oscillation index $\operatorname{moi}_Z(f)$ is defined. For sufficiently large residue-fie…

Let $F$ be an algebraically closed field of characteristic zero, let $(X,P)$ be an arbitrary germ over $F$, and let $Y$ be an affine $F$-scheme. Denote by…