Tropical adic spaces I: the continuous spectrum of a topological semiring
Netanel Friedenberg,
Kalina Mincheva
Abstract:Toward building tropical analogues of adic spaces, we study certain spaces of prime congruences as a topological semiring replacement for the space of continuous valuations on a topological ring. This requires building the theory of topological idempotent semirings, and we consider semirings of convergent power series as a primary example. We consider the semiring of convergent power series as a topological space by defining a metric on it. We check that, in tropical toric cases, the proposed objects carry mea… Show more
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