Dimensionality of tropical Chow groups
Abstract
We show that the existence of non-zero tropical forms of degree at least two implies that the tropical Chow group of points of an integral affine manifold is infinite-dimensional. This can be seen as a tropical analogue of classical results of Mumford and Roitman for Chow groups of smooth (complex) projective algebraic varieties. We also show that the existence of tropical 1-forms on integral affine surfaces does not imply infinite dimensionality by considering the case of a tropical Klein bottle.
Fields of Study & Subjects
Cocoa and Sweet Potato Agronomy
African Botany and Ecology Studies
Plant Diversity and Evolution
Publication details
- Journal / source
- Proceedings of the Royal Society of Edinburgh Section A Mathematics
- Pages
- 1–24
- Publication date
- 11 June 2026
- Language
- EN