Scientists / Open questions
Gerd Faltings
Arithmetic geometry; number theory
1986 Fields Medal
3 questions
Essential image of the p-adic Simpson correspondence: Faltings' conjecture that all semistable slope-zero Higgs bundles arise from genuine p-adic representations
Faltings' finiteness theorem for local cohomology up to order n: the missing converse on formal fibers, and lifting along -adic completion
Natural bounded families of Néron-points for the additive group and other non-proper groups in Faltings' Néron-model construction