The Newton stratification on deformations of local G-shtukas
The Newton stratification on deformations of local G-shtukas
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局部 G-shtukas 变形的牛顿分层
DOI：
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发表时间：
2008
期刊：
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通讯作者：
E. Viehmann
中科院分区：
文献类型：
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作者：
U. Hartl;E. Viehmann
摘要有界局部G-shtuka是具有额外结构的p-可除群的函数域模拟。我们描述了它们的变形和模空间。后者类似于p-可分群的Rapoport-Zink空间。这些模空间的基本格式是仿射Deligne-Lusztig簇。对于基本牛顿多边形，局部G-shtuka的泛变形中的闭牛顿层同构于对应的仿射Deligne-Lusztig簇在该点上的完备化。这给出了基本仿射Deligne-Lusztig簇的维上界并证明了它的等维性。
Abstract Bounded local G-shtukas are function field analogs for p-divisible groups with extra structure. We describe their deformations and moduli spaces. The latter are analogous to Rapoport–Zink spaces for p-divisible groups. The underlying schemes of these moduli spaces are affine Deligne–Lusztig varieties. For basic Newton polygons the closed Newton stratum in the universal deformation of a local G-shtuka is isomorphic to the completion of a corresponding affine Deligne–Lusztig variety in that point. This yields bounds on the dimension and proves equidimensionality of the basic affine Deligne–Lusztig varieties.