5 problems

Let $obreakforall obreaktext{?}$ For every $obreaktext{?}$

Parallel LTC amplification conjecture. There exists such a family for which the construction gives a parallel variant of the theorem on LTC amplification:

Let $X$ be a $2$-dimensional simplicial complex, let ${\mathcal{F}}$ be a sheaf on $X$, and use the notation of the modification process, including the subspaces $E_r$, $E'_r$,…

Let $q$ be a prime power, let $d\in\mathbb{N}$, and let $0<\gamma<1$. A $d$-dimensional measured poset $X$ is sparse when $|X(0)|=n$ and $|X(d)|=O(n)$, where the implied constant m…

Let $\mathcal{B}$ be the Bruhat–Tits building associated with $\mathrm{PGL}_{d}(F)$, where $F$ is a local field and $d\geq3$. For a finite quotient $X$ of $\mathcal{B}$, let…