论文标题
在离散的估值戒指和bruhat-tits建筑物上堆放着曲折矢量捆绑
Toric vector bundles over a discrete valuation ring and Bruhat-Tits buildings
论文作者
论文摘要
我们将等级$ r $ r $ torus equivariant矢量捆绑在折叠方案上的$ \ mathcal {e} $上的$ \ mathfrak {x} $上的离散估值环$ \ mathcal {o} $ \ mathcal {o} $，根据$ \ mathfrak $ \ gl（$ \ gl）的fan frous of分级线性linear maps $ nork $ \ the $ \ the $ \ mathfrak $ \ n of $ \ mathfraak $ \ n of the $ \ n Mathfraak $ \ n of（这是Klyachko一方面在田野上对圆环品种上的圆环矢量捆绑包的分类，另一方面，Mumford在$ \ Mathcal {o}上划分了摩托克方案上的earivariant Line捆绑包。我们还提供了一个简单的标准，即根据其分段线性映射，将$ \ Mathcal {e} $分配到圆环线束中。除其他外，这项工作奠定了研究曲线矢量束算术几何形状的基础。
We give a classification of rank $r$ torus equivariant vector bundles $\mathcal{E}$ on a toric scheme $\mathfrak{X}$ over a discrete valuation ring $\mathcal{O}$, in terms of graded piecewise linear maps $Φ$ from the fan of $\mathfrak{X}$ to the (extended) building of $GL(r)$. This is an extension of Klyachko's classification of torus equivariant vector bundles on toric varieties over a field on one hand, and Mumford's classification of equivariant line bundles on toric schemes over $\mathcal{O}$ on the other hand. We also give a simple criterion for equivariant splitting of $\mathcal{E}$ into a sum of toric line bundles in terms of its piecewise linear map. Among other things, this work lays the foundations for study of arithmetic geometry of toric vector bundles.
