10 problems

Let $G$ be a non-trivial finite étale tame $F$-group scheme, and let $H:BG(F)\to\mathbb{R}_{>0}$ be a height. Define the invariants $a(H)$ and $b(H)$ as in Definition 4.1. Quantita…

Refined secure-torsor counting conjecture. If $F$ is a number field, there exists $A>0$ such that

Secure-torsor counting conjecture. If $F$ is a number field, there exists $C>0$ such that

Let $k$ be a field of characteristic $p>0$, let $t$ be an indeterminate, and let $\operatorname{Spec} k(t)$ be the spectrum of its rational function field. A finite local $k$-group…

Tossici's conjecture.

Let $k$ be a perfect field of characteristic $p>0$, let $G=\alpha_p$, and let $V$ be a finite-dimensional representation of $G$ with quotient $V/G$. Let $H=\mathbb{Z}/p\mathbb{Z}$…

Verschiebung lower-bound conjecture. The essential dimension of $G$ over $k$ satisfies

Let $k$ be a field of positive characteristic, and let $G$ be a finite commutative unipotent group scheme over $k$. Let…

Let $E$ be an elementary abelian $p$-group of rank $n dgeq 2$, with $p3$. A stable type identifies Jordan types that differ only in the multiplicity of blocks of size $p$; the…

Let $E$ be an elementary abelian $p$-group of rank at least $2$, with $p>3$. A stable constant Jordan type is a Jordan type considered up to adding or removing summands of size $p$…