| Autor: |
Sébastien Boucksom, Walter Gubler, Florent Martin |
| Jazyk: |
English<br />French |
| Rok vydání: |
2021 |
| Předmět: |
|
| Zdroj: |
Épijournal de Géométrie Algébrique, Vol Volume 5 (2021) |
| Druh dokumentu: |
article |
| ISSN: |
2491-6765 |
| DOI: |
10.46298/epiga.2021.6908 |
| Popis: |
Let $L$ be a line bundle on a proper, geometrically reduced scheme $X$ over a non-trivially valued non-Archimedean field $K$. Roughly speaking, the non-Archimedean volume of a continuous metric on the Berkovich analytification of $L$ measures the asymptotic growth of the space of small sections of tensor powers of $L$. For a continuous semipositive metric on $L$ in the sense of Zhang, we show first that the non-Archimedean volume agrees with the energy. The existence of such a semipositive metric yields that $L$ is nef. A second result is that the non-Archimedean volume is differentiable at any semipositive continuous metric. These results are known when $L$ is ample, and the purpose of this paper is to generalize them to the nef case. The method is based on a detailed study of the content and the volume of a finitely presented torsion module over the (possibly non-noetherian) valuation ring of $K$. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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