Geometry of hyperfields
Geometry of hyperfields
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超场的几何
DOI：
10.1016/j.jalgebra.2020.11.005
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发表时间：
2017
影响因子：
0.9
通讯作者：
Jaiung Jun
中科院分区：
文献类型：
--
作者：
Jaiung Jun
给定一个方案 X over Z 和一个配备满足某些条件的拓扑的超域 H，我们赋予 H 有理点集合 X (H) 一个自然拓扑。然后我们证明：(1) 当 H 是克拉斯纳超场时，X (H) 同胚于 X 的底层空间；(2) 当 H 是热带超场且 X 是完全非阿基米德值场 k 上的有限型时，X (H) 同胚于 X 的 Berkovich 解析 X an 的底层空间；(3) 当 H 是符号超场时，X (H) 同胚于底层空间与 X 相关的实数方案 X r 的空间。
Given a scheme X over Z and a hyperfield H which is equipped with a topology which satisfies certain conditions, we endow the set X (H) of H-rational points with a natural topology. We then prove that;(1) when H is the Krasner hyperfield, X (H) is homeomorphic to the underlying space of X,(2) when H is the tropical hyperfield and X is of finite type over a complete non-Archimedean valued field k, X (H) is homeomorphic to the underlying space of the Berkovich analytification X an of X, and (3) when H is the hyperfield of signs, X (H) is homeomorphic to the underlying space of the real scheme X r associated with X.
影响因子：
2.5
作者：
Jeffrey Giansiracusa;Noah Giansiracusa
通讯作者：
Jeffrey Giansiracusa;Noah Giansiracusa