Weight-monodromy conjecture for p-adically uniformized varieties
Weight-monodromy conjecture for p-adically uniformized varieties
复制标题
p极均匀簇的权单性猜想
DOI：
10.1007/s00222-004-0395-y
复制
发表时间：
2003
影响因子：
3.1
通讯作者：
Tetsushi Ito
中科院分区：
文献类型：
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作者：
Tetsushi Ito
本文证明了由任意维Drinfeld上半空间p-基一致化的簇的权-单值猜想（Deligne关于单值过滤的纯性猜想）。证明的要素是证明霍奇标准猜想的一个特例，并应用Steenbrink，M。Saito对Rapoport-Zink的权谱序列进行了改进。作为一个应用，将我们的结果与Schneider-Stuhler的结果相结合，利用表示论不变量计算了p-基一致化簇的局部zeta函数.我们还考虑了一个p-adic模拟使用的重量谱序列的Mokrane。
The aim of this paper is to prove the weight-monodromy conjecture (Deligne’s conjecture on the purity of monodromy filtration) for varieties p-adically uniformized by the Drinfeld upper half spaces of any dimension. The ingredients of the proof are to prove a special case of the Hodge standard conjecture, and apply a positivity argument of Steenbrink, M. Saito to the weight spectral sequence of Rapoport-Zink. As an application, by combining our results with the results of Schneider-Stuhler, we compute the local zeta functions of p-adically uniformized varieties in terms of representation theoretic invariants. We also consider a p-adic analogue by using the weight spectral sequence of Mokrane.