Ax-Kochen-Ershov Principles and Artin's Conjecture

by Paulo Soto (Université Paris Cité)

Wednesday May 28, 2025, 5:00 PM → 7:00 PM Europe/Paris

Salle Fokko Du Cloux (ICJ)

It is known to be false that any homogeneous polynomial over Q_p of degree d in more than d^2 variables has a non-trivial zero in Q_p. However, a weaker version of this question remains true thanks to a transfer principle between Q_p and F_p((t)) "as p goes to infinity" and also by a theorem of Lang. We will explain this transfer principle due to Ax, Kochen and Ershov, which is itself a consequence of relative quantifier elimination of the theory of henselian valued fields of equicharacteristic 0. We will also introduce other transfer principles in some other theories of henselian valued fields.