Serre duality for rigid analytic spaces
Serre duality for rigid analytic spaces
复制标题
刚性分析空间的 Serre 对偶性
DOI：
10.1016/0019-3577(92)90011-9
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
M. Put
中科院分区：
文献类型：
--
作者：
M. Put
本文建立了非阿基米德值完备域K上刚性解析空间X → Y态射的对偶理论。为了使这些陈述和证明保持合理性，我们对Y是仿射的和X → Y是光滑的和适当的限制作了适当的处理。Stein空间的Chiarellotto [Ch]是本文的基础。一个重要的步骤是显示一个强形式的唯一性的剩余映射RES。进一步使用一个合适的定义上同调紧支持; R。Kiehl [K1]关于真映射的一些结果;[P]中引入的几何点;[BGR]中[K1，K2]的强G-拓扑.然而，对于研究真刚性解析流形，Serre-duality是不可缺少的。我们感谢B。Chiarellotto对手稿的仔细阅读，导致了论文的改进。
In this paper a duality theory for morphismX→Yof rigid analytic spaces over some non-archimedean valued complete fieldKis developed. In order to keep the statements and the proofs reasonable we make the restrictionsYis affinoid andX→Yis smooth and proper.The successful approach of B. Chiarellotto [Ch] for Stein spaces is the basis for this paper. An essential step is to show a strong form of unicity for the residue maps Res. One uses further a suitable definition for cohomology with compact support; the work of R. Kiehl [Kl] on proper mappings; geometric points as introduced in [P]; the strongG-topology of [K1,K2] in the version of [BGR].As one expects the paper is rather technical in nature and the results are not surprising. However for the investigation of proper rigid analytic manifolds the Serre-duality can not be missed. We thank B. Chiarellotto for his careful reading of the manuscript, which has led to improvements of the paper.