Formes différentielles réelles et courants sur les espaces de Berkovich
By Antoine Chambert-Loir, A. Ducros. 2012
124 citations recorded by the source corpus.
We define a theory of real $(p,q)$-forms and currents on Berkovich spaces which is parallel to the theory of differential forms on complex spaces: integrals, Poincare-Lelong formula, plurisubharmonic functions, positive currents, Chern forms of metrized line bundles...
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/0731383bf3b3e548b8b79ced2b0e91f2feeefcbc
How researchers see this paper
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In Applied Mathematics
- David Jensen
- Erwan Brugallé
- Omid Amini
- Joseph Rabinoff
- Matthew Baker
- Laura Demarco
- Mattias Jonsson
- Robert Rumely
In Geometry and Topology
- David Jensen
- Matthew Baker
- Omid Amini
- Joseph Rabinoff
- Erwan Brugallé
- Kristin M. Shaw
- Jascha Smacka
- Philipp Jell
Citations in the corpus
- Lifting harmonic morphisms II: tropical curves and metrized complexes (2014, background): “1In the present paper tropicalization is defined via Berkovich’s theory of analytic spaces (see also [Payne 2009; Baker et al. 2012; Chambert-Loir and Ducros 2012]).”
- Superforms, tropical cohomology, and Poincaré duality (2015, background): “Recently, superforms restricted to tropicalizations were used by Chambert-Loir and Ducros to construct real-valued differential forms on analytic spaces in the sense of Berkovich [CLD12].”
- Degeneration of Linear Series from the Tropical Point of View and Applications (2015, result): “Using a result of Heinz [Hei04] and the recent work of Chambert-Loir– Ducros [CLD12] and Gubler–Kunnemann [GK14] on non-Archimedean Arakelov theory, one can show that, as in the Archimedean case, µC is obtained by pulling back the curvature form of a canonical translation-invariant metric on J via a”