Non-archimedean integrals as limits of complex integrals

Abstract

We explain how non-archimedean integrals considered by Chambert-Loir and Ducros naturally arise in asymptotics of families of complex integrals. To perform this analysis we work over a non-standard model of the field of complex numbers, which is endowed at the same time with an archimedean and a non-archimedean norm. Our main result states the existence of a natural morphism between bicomplexes of archimedean and non-archimedean forms which is compatible with integration.

69 pages

References in corpus (3)

• Espaces de Berkovich, polytopes, squelettes et théorie des modèles
• Gromov-Hausdorff limits of flat Riemannian surfaces
• Tropical Geometric Compactification of Moduli, II - $A_g$ case and holomorphic limits -

Cited by in corpus (1)

• Gromov-Hausdorff limits of flat Riemannian surfaces