Hilbert's tenth problem via additive combinatorics

2024/12/02 by Koymans, Peter, Pagano, Carlo · 6 citations
#FOS: Mathematics #Logic (math.LO) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2412.01768

Abstract

For all infinite rings R that are finitely generated over ℤ, we show that Hilbert's tenth problem has a negative answer. This is accomplished by constructing elliptic curves E without rank growth in certain quadratic extensions L/K. To achieve such a result unconditionally, our key innovation is to use elliptic curves E with full rational 2-torsion which allows us to combine techniques from additive combinatorics with 2-descent.

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