<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332023000100113</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v30i1.52266</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Superficies elípticas y el décimo problema de Hilbert]]></article-title>
<article-title xml:lang="en"><![CDATA[Elliptic surfaces and Hilbert&#8217;s tenth problem]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Pasten]]></surname>
<given-names><![CDATA[Hector]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Pontificia Universidad Católica de Chile Departamento de Matemáticas Facultad de Matemáticas]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2023</year>
</pub-date>
<volume>30</volume>
<numero>1</numero>
<fpage>113</fpage>
<lpage>120</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332023000100113&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332023000100113&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332023000100113&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Es sabido que se obtendría una solución negativa al decimo problema de Hilbert para el anillo de enteros OF de un campo de números F si Z fuera diofantino en OF . Denef y Lipshitz conjeturaron que esto ultimo ocurre para todo F. En esta nota se demuestra que la conjetura de Denef y Lipshitz es consecuencia de una conocida conjetura sobre superficies elípticas.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract A negative solution to Hilbert&#8217;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.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Decimo problema de Hilbert]]></kwd>
<kwd lng="es"><![CDATA[anillos de enteros]]></kwd>
<kwd lng="es"><![CDATA[superficies elípticas]]></kwd>
<kwd lng="es"><![CDATA[curvas elípticas.]]></kwd>
<kwd lng="en"><![CDATA[Hilbert&#8217;s tenth problem]]></kwd>
<kwd lng="en"><![CDATA[rings of integers]]></kwd>
<kwd lng="en"><![CDATA[elliptic surfaces]]></kwd>
<kwd lng="en"><![CDATA[elliptic curves.]]></kwd>
</kwd-group>
</article-meta>
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