ScalingStacks

Remark 7.7 [037J]

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Remark 7.7

One can define the irreducible components of an analytic space (see [Con99]). A compact analytic space ZZ has finitely many irreducible components ZiZ_{i}. Then we define the cycle cyc⁡(Z){\rm cyc}(Z) associated to ZZ as a positive formal ℤ{\mathbb{Z}}-linear combination of the irreducible components ZiZ_{i} by restriction to affinoid subdomains and then by glueing (see [Gu98], §2). One can show that the weighted nn-dimensional polyhedral complex (φtrop)∗​(cyc⁡(Z))({\varphi_{\rm trop}})_{*}({\rm cyc}(Z)) depends only on cyc⁡(Z){\rm cyc}(Z) and this dependence is linear. We leave the details to the reader.

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