Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

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Elliptic surfaces and Hilbert’s tenth problem
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Keywords

Décimo problema de Hilbert
Anillos de enteros
Superficies elípticas
Curvas elípticas
Hilbert’s tenth problem
Rings of integers
Elliptic surfaces
Elliptic curves

How to Cite

Pastén, H. (2023). Elliptic surfaces and Hilbert’s tenth problem. Revista De Matemática: Teoría Y Aplicaciones, 30(1), 113–120. https://doi.org/10.15517/rmta.v30i1.52266

Abstract

A negative solution to Hilbert’s tenth problem for the ring of integers OF of a number field F would follow if Z were Diophantine in OF. Denef and Lipshitz conjectured that the latter occurs for every number field F. In this note we show that the conjecture of Denef and Lipshitz is a consequence of a well-known conjecture on elliptic surfaces.

https://doi.org/10.15517/rmta.v30i1.52266
PDF (Español (España))

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