2 papers
math.NT2025
Diophantine sets
Bhargav Bhatt, Bjorn Poonen
Diophantine subsets of play a key role in the negative answer to Hilbert's tenth problem. The definition of diophantine set generalizes in several ways to other commut…
math.NT2025
Rank stability makes rings of integers diophantine
Bjorn Poonen
The recent negative answer to Hilbert's tenth problem over rings of integers relies on a theorem that for every extension of number fields , if there is an abelian variety …