Peter Koymans

Constructing Jacobians of rank 1

Abstract Let 𝐾 be a number field, let g ≥ 1 g\geq 1 be an integer and let f ⁢ ( x ) = ( x − a 1 ) ⁢ ⋯ ⁢ ( x − a 2 ⁢ g + 1 ) ∈ O K ⁢ [ x ] see text f(x)=(x-a_{1})\cdots(x-a_{2g+1})\in O_{K}[x] be a polynomial that splits into 2 ⁢ g + 1 2g+1 distinct linear factors. Write 𝐶 for the...

Hilbert’s tenth problem via additive combinatorics

For all infinite rings <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding="application/x-tex">R</mml:annotation> </mml:semantics> </mml:math> </inline-...