We discuss some problems of definability and decidability over rings of integers of algebraic extensions of ℚ. In particular, we show that for a large class of fields K there is a simple formula defining rational integers over OK. Below, UK is the group of units of OK.
RK= { x | ∀ ε ∈ UK \ {1} ∃ δ ∈ UK : x ≡ (δ-1)/(ε-1) mod (ε-1) }.
This talk is based on a joint paper with Barry Mazur and Karl Rubin.
This video is part of the Number Theory Web Seminar series.
