<?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>0034-7426</journal-id>
<journal-title><![CDATA[Revista Colombiana de Matemáticas]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.colomb.mat.]]></abbrev-journal-title>
<issn>0034-7426</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0034-74262012000200005</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[The Brauer Group of K3 Covers]]></article-title>
<article-title xml:lang="es"><![CDATA[El grupo de Brauer de K3 cubrimientos]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[MARTÍNEZ]]></surname>
<given-names><![CDATA[HERMES]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad Sergio Arboleda  ]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>15</day>
<month>12</month>
<year>2012</year>
</pub-date>
<pub-date pub-type="epub">
<day>15</day>
<month>12</month>
<year>2012</year>
</pub-date>
<volume>46</volume>
<numero>2</numero>
<fpage>185</fpage>
<lpage>204</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0034-74262012000200005&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0034-74262012000200005&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0034-74262012000200005&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[In this paper we study the injectivity of the induced morphism on the Brauer groups &pi;*: \Br'(Y) &rarr; \Br'(X) given by the K3 cover &pi;:X &rarr; Y of the Enriques surface Y.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[En este artículo estudiamos la inyectividad del morfismo inducido sobre los grupos de Brauer &pi;*: \Br(Y) &rarr; \Br(X) dado por el K3 cubrimiento &pi;:X &rarr; Y de la superficie de Enriques Y.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Brauer group]]></kwd>
<kwd lng="en"><![CDATA[K3 surface]]></kwd>
<kwd lng="en"><![CDATA[Hochschild--Serre spectral sequence]]></kwd>
<kwd lng="es"><![CDATA[Grupo de Brauer]]></kwd>
<kwd lng="es"><![CDATA[superficie K3]]></kwd>
<kwd lng="es"><![CDATA[sucesión espectral de Hochschild--Serre]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[  <font size="2" face="verdana">      <p> <b> <font size="4">     <center> The Brauer Group of K3 Covers </center> </font> </b> </p>      <p> <b> <font size="3">     <center> El grupo de Brauer de K3 cubrimientos </center> </font> </b> </p>      <p>     <center> HERMES MART&Iacute;NEZ<sup>1</sup> </center> </p>      <p> <sup>1</sup>Universidad Sergio Arboleda, Bogot&aacute;, Colombia. Email: <a href="mailto:hermes.martinez@usa.edu.co">hermes.martinez@usa.edu.co</a>     <br> </p>  <hr size="1">      <p> <b>     ]]></body>
<body><![CDATA[<center> Abstract </center> </b> </p>      <p> In this paper we study the injectivity of the induced morphism on the Brauer groups <i>&pi;<sup>*</sup>: \Br'(Y) &rarr; \Br'(X)</i> given by the K3 cover <i>&pi;:X &rarr; Y</i> of the Enriques surface <i>Y</i>. </p>      <p> <b> Key words: </b> Brauer group, K3 surface, Hochschild--Serre spectral sequence. </p>  <hr size="1">  <i>2000 Mathematics Subject Classification: 14J28, 16K50, 20J062.</i>  <hr size="1">      <p> <b>     <center> Resumen </center> </b> </p>      <p> En este art&iacute;culo estudiamos la inyectividad del morfismo inducido sobre los grupos de Brauer <i>&pi;<sup>*</sup>: \Br(Y) &rarr; \Br(X)</i> dado por el K3 cubrimiento <i>&pi;:X &rarr; Y</i> de la superficie de Enriques <i>Y</i>. </p>      <p> <b> Palabras clave: </b> Grupo de Brauer, superficie K3, sucesi&oacute;n espectral de Hochschild--Serre. </p>  <hr size="1">      <p> Texto completo disponible en <a href="pdf/rcm/v46n2/v46n2a05.pdf">PDF</a> </p>  <hr size="1">      <p> <b> <font size="3"> References </font> </b> </p>       <!-- ref --><p> &#91;1&#93; W. Barth, K. Hulek, C. Peters, and A. V. d. Ven, <i>Compact Complex Surfaces</i>, Vol. 4 of <i>Modern Surveys in Mathematics</i>, 2nd edn, Springer Verlag, Berlin, Germany,    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000022&pid=S0034-7426201200020000500001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> 2004. </p>      <!-- ref --><p> &#91;2&#93; A. Beauville, 'On the Brauer Group of Enriques Surfaces', <i>Math. Research Letters</i> <i>16</i>,  (2009), 927-934.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000024&pid=S0034-7426201200020000500002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      <!-- ref --><p> &#91;3&#93; D. Harari and A. Skorobogatov, 'Non-abelian Descent and the Arithmetic of Enriques Surfaces', <i>Int. Math. Res. Not.</i>, 52 (2005), 3203-3228.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000026&pid=S0034-7426201200020000500003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      <!-- ref --><p> &#91;4&#93; K. Ireland and M. Rosen, <i>A Classical Introduction to Modern Number Theory</i>, Vol. 84 of <i>Graduate Texts in Mathematics</i>, Springer-Verlag, New York, USA,    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000028&pid=S0034-7426201200020000500004&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> 1990. </p>      <!-- ref --><p> &#91;5&#93; J. S. Milne, <i>Lectures on Etale Cohomology (v2.20)</i>, (2012). Available at http://www.jmilne.org/math/ &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000030&pid=S0034-7426201200020000500005&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> &#91;6&#93; D. Morrison, 'On K3 Surfaces with large Picard Number', <i>Invent. Math.</i> <i>75</i>, 1 (1984), 105-121.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000031&pid=S0034-7426201200020000500006&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      ]]></body>
<body><![CDATA[<!-- ref --><p> &#91;7&#93; D. Naie, 'Special Rank Two Vector Bundles over Enriques Surfaces', <i>Mathematische Annalen</i> <i>300</i>, 1 (1994), 297-316.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000033&pid=S0034-7426201200020000500007&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      <!-- ref --><p> &#91;8&#93; V. V. Nikulin, 'Factor Groups of Groups of Automorphisms of Hyperbolic Forms with respect to Subgroups Generated by 2-reflections', <i>J. Soviet Math.</i> <i>22</i>,  (1983), 1401-1476. English Translation &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000035&pid=S0034-7426201200020000500008&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> &#91;9&#93; H. Ohashi, 'On the Number of Enriques Quotients of a K3 Surface', <i>Publ. Res. Inst. Math. Sci.</i> <i>43</i>, 1 (2007), 181-200.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000036&pid=S0034-7426201200020000500009&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      <!-- ref --><p> &#91;10&#93; R. L. E. Schwarzenberger, 'Vector Bundles on Algebraic Surfaces', <i>Proc. London Math. Soc.</i> <i>3</i>, 11 (1961), 601-622.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000038&pid=S0034-7426201200020000500010&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      <!-- ref --><p> &#91;11&#93; C. Weibel, <i>An Introduction to Homological Algebra</i>, Cambridge University Press, Cambridge University Press, Cambridge, UK,    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000040&pid=S0034-7426201200020000500011&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> 1994. </p>  <hr size="1">      <center> <b>(Recibido en mayo de 2012. Aceptado en octubre de 2012)</b> </center> <hr size="1">      ]]></body>
<body><![CDATA[<p> Este art&iacute;culo se puede citar en <i>LaTeX</i> utilizando la siguiente referencia bibliogr&aacute;fica de <i>BibTeX</i>: </p> <code><font size="2" face="verdana"> @ARTICLE{RCMv46n2a05,    <br>  &nbsp;&nbsp;&nbsp; AUTHOR &nbsp;= {Mart&iacute;nez, Hermes},    <br>  &nbsp;&nbsp;&nbsp; TITLE &nbsp; = {{The Brauer Group of K3 Covers}},    <br>  &nbsp;&nbsp;&nbsp; JOURNAL = {Revista Colombiana de Matem&aacute;ticas},    <br> &nbsp;&nbsp;&nbsp; YEAR &nbsp;&nbsp; = {2012},    <br> &nbsp;&nbsp;&nbsp; volume &nbsp;= {46},    <br> &nbsp;&nbsp;&nbsp; number &nbsp;= {2},    <br> &nbsp;&nbsp;&nbsp; pages &nbsp; = {185--204}    <br> } </font></code>  <hr size="1"> </font>      ]]></body><back>
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