Franziska Jahnke (Universität Münster)

Frankfurter Seminar

Abstract: Under which circumstances can we use insights about fields of positive characteristic to understand fields of characteristic 0 (and conversely)?
Classical methods to transfer results between fields of different  characteristics are the Lefshetz principle and the Ax Kochen/Ershov Theorem which states that asymptotically, the theory of the p-adic numbers ℚ_p and of power series fields 𝔽_p((t)) coincide. Tilting perfectoid fields gives a transfer principle between certain henselian fields of mixed characteristic and their positive characteristic counterparts and vice versa. In this talk, we survey various transfer principles and present a model-theoretic approach to tilting via ultraproducts, which allows us to transfer many first-order properties between a perfectoid field and its tilt.