13 problems

Let $F$ be the tuple of functions and let $B_F^{\mathbf{m}_1,\dots,\mathbf{m}_p}$ denote the associated ideal in the variables $s_1,\dots,s_r$, where…

Let $F=(f_1,\ldots,f_r)$ be a tuple of polynomials, let $Z_F^{mot}(s_1,\ldots,s_r)$ be its multivariable motivic zeta function, and let $B_F\subset\mathbb{C}[s_1,\ldots,s_r]$ be it…

Let $X$ be the underlying space, let $\mathcal{M}$ be a regular holonomic $\mathscr{D}_X$-module, and let $\mathcal{N}_0$ be the associated module. For a monoid ideal…

Let $F=(f_1,\ldots,f_r)$ be a tuple with multivariable Bernstein–Sato ideals $B_F^{\bm m}$ indexed by $\bm m\in\mathbb{N}^r$, and let $\bm e_j$ denote the $j$th standard basis vect…

Bernstein–Sato ideal conjecture. The Bernstein–Sato ideal $B_F$ is generated by products of linear polynomials of this type, and the image under $\operatorname{Exp}$ of the zero lo…

Generalized monodromy conjecture. The following assertions hold: (i) the image under $\operatorname{Exp}$ of the polar locus of the motivic zeta function of $F$ is $S_F$; and (ii)…

Rationality conjecture for Bernstein-Sato ideals. The ideal $B_{F_\mathbb{C}}^a$ is generated by polynomials with coefficients in $\mathbb{Q}$; consequently, the same polynomials g…

Let $F=(f_1,\ldots,f_r)$ be a tuple of polynomials and let $B_F\subset \mathbb{C}[s_1,\ldots,s_r]$ denote its Bernstein-Sato ideal. The ideal is said to be generated by products of…

Let $F=(f_1,\ldots,f_r):X\rightarrow\mathbb{C}^r$ be a collection of non-invertible analytic functions on a complex manifold such that $f^{-1}(0)$ admits a finite Whitney stratific…

Let $F=(f_1, 3ellots,f_r)$, let $M\in\mathbb{N}^{p\times r}$ be non-zero, let ${\bf m}\in\mathbb{N}^p$, and let $F^M$ and the monomial maps $\phi_M$ be defined as in the source. Wr…

Let $F=(f_1, 3ellots,f_r)$ with $0\ne f_j\in\mathbb{C}[x_1, 3ellots,x_n]$, let $\mu:Y\to X$ be a log resolution of $\prod_jf_j$, and write $a_{i,j}$ for the order of vanishing of…

Let $F=(f_1, 3ellots,f_r)$, where each $f_j$ is a not necessarily reduced central hyperplane arrangement in $\mathbb{C}^n$ of degree $d_j$, and suppose that $\prod_{j=1}^rf_j$ is a…

Let $F=(f_1, 3ellots,f_r)$ be a collection of non-zero polynomials on $X=\mathbb{C}^n$, let $D=\bigcup_{j=1}^rV(f_j)$, and let $B_{F,x}$ denote the local Bernstein-Sato ideal at…