MathOverflow

In Zink's paper The display of a formal $p$-divisible group (link at Zink's page), he states that he has an exact sequence$$0\rightarrow \widehat{W}(N)\xrightarrow{\cdot F-1}\widehat{W}(N)\xrightarrow{\mathrm{hex}}\widehat{\mathbb{G}}_m(N)\rightarrow...

I want to find a proof that the ratio $R(t)$ below is decreasing in $t>0$.$$R(t)=\frac{\sum_{n=1}^\infty n^2e^{-4n^2t}}{\sum_{n=1}^\infty n^2e^{-n^2t}}$$This is the ratio of two hitting times for a Brownian motion. I haven't had any success using...

Let $\mathcal{P} \subseteq \mathbb{R}^n$ be a polytope with non-empty interior. It is given as an intersection of $m$ half-spaces. From a point in its interior, assume that there are some lines through the vertices of $\mathcal{P}$. Obtain the polytopes...

Let $C_s$ be the quiver $ 1 \rightarrow 2 \rightarrow \cdots \rightarrow s-1 \rightarrow s \rightarrow 1$, i.e. the cyclic quiver with s vertexes and s arrows.Then, we denote by $k C_s$ the path algebra and by $J$ the radical, which is the ideal generated...