Tropical Approaches to Arakelov Theory (A05)

• Subject Area: Mathematics
• Term: since 2014
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 224262486

We develop an analytic approach to non-archimedean Arakelov geometry based on the real-valued differential forms and currents on non-archimedean analytic spaces introduced by Chambert-Loir and Ducros. Guiding problems are an adelic approach to Arakelov theory, an unconditional construction of height pairings for homologically trivial algebraic cycles, a detailed investigation of the case of toric varieties, the study of metrized vector bundles, and the construction of non-archimedean Green currents for algebraic cycles. Furthermore, delta-forms and b-divisors will be considered.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1085: Higher Invariants – Interactions between Arithmetic Geometry and Global Analysis
• Applicant Institution: Universität Regensburg
• Project Heads: Professor Dr. Walter Gubler; Professor Dr. Klaus Künnemann