I've made further progress, following along the same lines as vonfritz:
- the official Arch kernel does not work
- I compiled my own kernel from the source at
https://github.com/amery/linux-allwinner(using the default sun4i_defconfig configuration); that boots OK.
I think the Arch kernel is from the same source, but a slightly earlier version
I've got X working fine. You need to load the "lcd" and "hdmi" modules, then you can start X from an ssh console. Unfortunately there's no framebuffer console, so nothing appears on the HDMI until you start X; this seems to be a known bug that people are working on.