论文标题
bruhat-tits的多面体压缩，准还原群的建筑物
Polyhedral compactifications of Bruhat-Tits buildings of quasi-reductive groups
论文作者
论文摘要
鉴于使用Berkovich几何形状在本地字段$ k $上进行了准级$ g $，我们展示了$ g（k）$ - bruhat-tits建造$ \ mathcal b（g，k）$的bruhat-tits的压实，由Solleveld andLourenço建造和研究。紧凑过程包括在分析中映射建筑物$ g^{\ mathrm {an}} $的$ g $，然后将此地图与$ g^{\ mathrm {an}} $投影的投影构成其（一般非compact）pseudo-flag varieties $（for $ p）$（for $ p）在$ g $的伪 - 撒布代谢子组之间。这概括了伯科维奇，然后是雷米，瑟利尔和沃纳的先前建筑。 为了定义嵌入，由于卢梭对Bruhat-tits建筑物的功能相对于现场扩展的功能，因此我们被导致对结果的准还原性背景进行部分扩展，这具有独立的利益。 最后，我们通过研究这些紧凑型无穷大的几何形状来得出结论。边界被证明是分层的，每个阶层都是同构的同构，与假parabolic亚组的最大准重还原商的bruhat-tits构建。
Given a quasi-reductive group $G$ over a local field $k$, using Berkovich geometry, we exhibit a family of $G(k)$-equivariant compactifications of the Bruhat-Tits building $\mathcal B(G, k)$, constructed and investigated by Solleveld and Lourenço. The compactification procedure consists in mapping the building in the analytification $G^{\mathrm{an}}$ of $G$, then composing this map with the projections from $G^{\mathrm{an}}$ to its (in general non-compact) pseudo-flag varieties $(G/P)^{\mathrm{an}}$, for $P$ ranging among the pseudo-parabolic subgroups of $G$. This generalises previous constructions of Berkovich, then Rémy, Thuillier and Werner. To define the embedding, we are led to giving a partial extension to the quasi-reductive context of results due to Rousseau on the functoriality of Bruhat-Tits buildings with respect to field extensions, which are of independent interest. Finally, we conclude by investigating the geometry at infinity of these compactifications. The boundaries are shown to be stratified, each stratum being equivariantly homeomorphic to the Bruhat-Tits building of the maximal quasi-reductive quotient of a pseudo-parabolic subgroup.
