2017/07/28 by Jun, Jaiung · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1707.09348
Given a scheme X over ℤ and a hyperfield H which is equipped with topology, 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 analytificaiton X^\textrman of X, and (3) when H is the hyperfield of signs, X(H) is homeomorphic to the underlying space of the real scheme Xr associated with X.