Honda–Tate theory for Shimura varieties
Honda–Tate theory for Shimura varieties
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DOI：
10.1215/00127094-2021-0063
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发表时间：
2022-01
影响因子：
2.5
通讯作者：
M. Kisin;Keerthi Madapusi Pera;S. Shin
中科院分区：
文献类型：
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作者：
M. Kisin;Keerthi Madapusi Pera;S. Shin
Hodge型的志村变种是阿贝尔变种具有一定的Hodge循环集合的模空间。我们证明了在这些变异上的牛顿地层是非空的，只要对应的群G在p处是拟分裂的，在这种情况下证实了Fargues和Rapoport的一个猜想。在相同的条件下，我们推测在这样一个变种上的每一个模p同系类都包含一个特殊点的约化。这是对本田-泰特理论的改进。我们对PEL型的Shimura变种证明了这一猜想的很大一部分。我们的结果没有假设志村品种的一个好的积分模型的可用性。特别地，G基团可以在p点被分叉。
A Shimura variety of Hodge type is a moduli space for abelian varieties equipped with a certain collection of Hodge cycles. We show that the Newton strata on such varieties are non-empty provided the corresponding group G is quasi-split at p, confirming a conjecture of Fargues and Rapoport in this case. Under the same condition, we conjecture that every mod p isogeny class on such a variety contains the reduction of a special point. This is a refinement of Honda-Tate theory. We prove a large part of this conjecture for Shimura varieties of PEL type. Our results make no assumption on the availability of a good integral model for the Shimura variety. In particular, the group G may be ramified at p.