We prove that an admissible normal function over a surface and the zero section simultaneously extend to sections of a log Néron model. This gives a new proof of the surface base case of the algebraicity of zero loci of admissible normal functions.
"Log Néron models over surfaces, II." Hokkaido Math. J. 44 (3) 365 - 385, October 2015. https://doi.org/10.14492/hokmj/1470053369