A.4. Hybrid geometry over ℂ [018I]
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A.4. Hybrid geometry over
If is a scheme of finite type over , we denote by its analytification with respect to the usual absolute value , by its analytification with respect to the trivial absolute value, and by its analytification with respect to the hybrid norm .
From the structure morphism we obtain a continuous map . The fiber is equal to the analytification of with respect to the multiplicative norm on . In particular, we have canonical identifications and . For , the fiber is also homeomorphic to . In fact, we have a a homeomorphism
see [Berk09, Lemma 2.1].