Alternative Links zum Volltext:DOIVerlag
| Dokumentenart: | Artikel |
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| Titel eines Journals oder einer Zeitschrift: | Mathematische Zeitschrift |
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| Verlag: | SPRINGER HEIDELBERG |
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| Ort der Veröffentlichung: | HEIDELBERG |
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| Band: | 293 |
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| Nummer des Zeitschriftenheftes oder des Kapitels: | 1-2 |
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| Seitenbereich: | S. 443-474 |
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| Datum: | 2019 |
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| Institutionen: | Mathematik |
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| Identifikationsnummer: | | Wert | Typ |
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| 10.1007/s00209-018-2205-z | DOI |
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| Stichwörter / Keywords: | GEOMETRY; Subharmonic functions; Superforms; Berkovich spaces; Tropical geometry |
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| Dewey-Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
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| Status: | Veröffentlicht |
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| Begutachtet: | Ja, diese Version wurde begutachtet |
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| An der Universität Regensburg entstanden: | Ja |
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| Dokumenten-ID: | 48214 |
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Zusammenfassung
We show that a continuous function on the analytification of a smooth proper algebraic curve over a non-archimedean field is subharmonic in the sense of Thuillier if and only if it is psh, i.e. subharmonic in the sense of Chambert-Loir and Ducros. This equivalence implies that the property psh for continuous functions is stable under pullback with respect to morphisms of curves. Furthermore, we ...
Zusammenfassung
We show that a continuous function on the analytification of a smooth proper algebraic curve over a non-archimedean field is subharmonic in the sense of Thuillier if and only if it is psh, i.e. subharmonic in the sense of Chambert-Loir and Ducros. This equivalence implies that the property psh for continuous functions is stable under pullback with respect to morphisms of curves. Furthermore, we prove an analogue of the monotone regularization theorem on the analytification of P1 and Mumford curves using this equivalence.
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