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Gromov compactness in non-archimedean analytic geometry.
- Source :
- Journal für die Reine und Angewandte Mathematik; 2018, Vol. 2018 Issue 741, p179-210, 32p
- Publication Year :
- 2018
-
Abstract
- Gromov’s compactness theorem for pseudo-holomorphic curves is a foundational result in symplectic geometry. It controls the compactness of the moduli space of pseudo-holomorphic curves with bounded area in a symplectic manifold. In this paper, we prove the analog of Gromov’s compactness theorem in non-archimedean analytic geometry. We work in the framework of Berkovich spaces. First, we introduce a notion of Kähler structure in non-archimedean analytic geometry using metrizations of virtual line bundles. Second, we introduce formal stacks and non-archimedean analytic stacks. Then we construct the moduli stack of non-archimedean analytic stable maps using formal models, Artin’s representability criterion and the geometry of stable curves. Finally, we reduce the non-archimedean problem to the known compactness results in algebraic geometry. The motivation of this paper is to provide the foundations for non-archimedean enumerative geometry. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00754102
- Volume :
- 2018
- Issue :
- 741
- Database :
- Complementary Index
- Journal :
- Journal für die Reine und Angewandte Mathematik
- Publication Type :
- Academic Journal
- Accession number :
- 131059862
- Full Text :
- https://doi.org/10.1515/crelle-2015-0077