Number theory · Oct 6, 2026

Function-field reconstruction from Milnor K-theory and Galois data

Reconstructs function fields of transcendence degree at least two over algebraically closed constants from K1M/ℓK^{\mathrm M}_1/\ell, K2M/ℓK^{\mathrm M}_2/\ell, and their product. These data recover the perfect closure and constants when ℓ differs from the characteristic, and the original field and its named base in equal characteristic. Also proves Bogomolov–Pop reconstruction from abelian-by-central pro-ℓ Galois data away from the characteristic.

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