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Central extensions of group schemes

In the category of groups, it is elementary that all central extensions of a cyclic group are abelian. Is the same true, in the category of (finite?) group schemes over a field $k$, for central ...
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Fixed points of the Borel-Serre compactification

Let $\Gamma$ be an arithmetic group and $X$ its symmetric space. Borel-Serre constructed a space $\bar{X} \supset X$ such that $\bar{X}/\Gamma$ is a compactification of $X/\Gamma$ [Corners and ...
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Geometry Realization of Homology Class

Hello! My question is about the realization of homology class. The definition of the realizaion of homology class is: for manifold M and a homology class $z\in H_k(M)$, k is an integer. If we find a ...
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Gradient estimates for subsolutions of elliptic equations

Let $M$ be a Riemannian manifold. Assume $u \in C^\infty(M)$ such that $u>0$ and $\Delta u + \lambda u = 0,$ where $\lambda \geq 0$. There is a poinwise estimate for $|\nabla u|$ in Peter Li's ...
If $P$ and $Q$ are two sufficiently general points on a cubic surface, the line between them intersects the cubic surface at a unique third point, $f(P,Q)$. This gives a binary operation on (generic) ...