We construct invariants of birational maps with values in the Kontsevich--Tschinkel group
and in the truncated Grothendieck groups of varieties. These invariants are morphisms of …

We construct an existentially undecidable complete discretely valued field of mixed
characteristic with existentially decidable residue field and decidable algebraic part …

In this paper, we characterize NIP henselian valued fields modulo the theory of their residue
field, both in an algebraic and in a model-theoretic way. Assuming the conjecture that every …

We study the model theory of finitely ramified henselian valued fields of fixed initial
ramification, obtaining versions of the Ax–Kochen–Ershov principle as follows. We identify …

In the spirit of the Ax-Kochen-Ershov principle, we show that in certain cases the burden of a
Henselian valued field can be computed in terms of the burden of its residue field and that of …

The thesis addresses certain problems in the model theory of henselian fields, with a special
focus on decidability. Some new methods are introduced along the way, which are of …

We prove a relative decidability result for perfectoid fields. This applies to show that the
fields ℚ p (p 1∕ p∞) and ℚ p (ζ p∞) are (existentially) decidable relative to the perfect hull …

We show a transfer principle for the property that all types realised in a given elementary
extension are definable. It can be written as follows: a Henselian valued field is stably …

Let K be an NIP field and let v be a Henselian valuation on K. We ask whether (K, v) is NIP
as a valued field. By a result of Shelah, we know that if v is externally definable, then (K, v) is …

Assuming a certain form of resolution of singularities, we prove a general existential Ax-
Kochen/Ershov principle for tamely ramified fields in all characteristics. This specializes to …