6 problems

Let $A$ be a polynomial ring, let $I\subseteq A$ be a $\mathbb{Z}^m$-graded Cartwright–Strumfels ideal, let $\operatorname{gin}(I)$ be its $\mathbb{Z}^m$-graded generic initial ide…

Let $c\in\mathbb{N}$ and $d\in\mathbb{N}_{\geq2}$, let $W=W_d$ be the Witt function, and let $\mathfrak{f}_{c,d}$ be the free nilpotent Lie ring of class $c$ on $d$ generators. Wri…

Assume the uniformity conjecture, so that the reduced graded ideal zeta function $\zeta_{\mathfrak{f}_{c,d},\operatorname{red}}^{\triangleleft_{\operatorname{gr}}}(Y)$ is defined.…

Let $c\in\mathbb{N}$ and $d\in\mathbb{N}_{\geq2}$, let $\mathfrak{f}_{c,d}$ be the free nilpotent Lie ring of class $c$ on $d$ generators, and put…

Assume the uniformity conjecture, and define the reduced graded ideal zeta function by … Let $r=\sum_{i=1}^cW_d(i)$ and $[N]_0=\{0,\ldots,N\}$. Reduced zeta-function conjecture. Th…

Let $c\in\mathbb{N}$ and $d\in\mathbb{N}_{\geq 2}$. Let $\mathfrak{f}_{c,d}$ be the free nilpotent Lie ring of class $c$ on $d$ generators, and let $\mathfrak{o}$ be a finite exten…