<?xml version="1.0" encoding="UTF-8" ?>
<oai_dc:dc schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
<dc:title lang="ca-ES">$p$-adic deformations of cohomology classes of subgroups of $GL(n,\mathbb{Z})$</dc:title>
<dc:creator>Ash, Avner</dc:creator>
<dc:creator>Stevens, G.</dc:creator>
<dc:description lang="ca-ES">We construct $p$-adic analytic families of $p$-ordinary cohomology classes in the cohomology of arithmetic subgroups of $GL(n)$ with coefficients in a family of representation spaces for $GL(n)$. These analytic families are parametrized by the highest weights of the coefficient modules. More precisely, we consider the cohomology of a compact $\mathbb{Z}_p$-module $\mathbb{D}$ of $p$-adic measures on a certain homogeneous space of $GL(n,\mathbb{Z}_p)$. For any dominant weight $\lambda$ with respect to a fixed choice $(B, T)$ of a Borel subgroup $B$ and a maximal split torus $T\subseteq B$ and for any finite "nebentype" character $\epsilon : T(\mathbb{Z}_p)\longrightarrow\mathbb{Z} ^x_p$ we construct a $\mathbb{Z}_p$-map from $\mathbb{D}$ to $V_{\lambda,\epsilon}$. These maps are equivariant for commuting actions of $T(\mathbb{Z}_p)$ and $\Gamma_\nu$ where $\Gamma_\nu \subseteq GL(n, \mathbb{Z})$ is a congruence subgroup analogous to $\Gamma_0(p^\nu)$ where $p^\nu$ is the conductor of $\epsilon$ . We also make the matrix $\pi := diag(1, p, p^2,\dots , p^{n-1})$ act equivariantly on all these modules. We obtain a $\Lambda := \mathbb{Z}_p[[T(\mathbb{Z}_p)]]$-module structure on $H^\ast(\Gamma,\mathbb{D})$ and Hecke actions on $H^\ast(\Gamma,\mathbb{D})$ and $H^\ast(\Gamma_\nu, V_{\lambda,\epsilon})$ with Hecke equivariant maps $\phi_{\lambda,\epsilon} : H^\ast(\Gamma,\mathbb{D})\longrightarrow H^\ast(\Gamma_\nu, V_{\lambda,\epsilon})$, where $\Gamma$ is a congruence subgroup of $GL(n,\mathbb{Z})$ of level prime to $p$ and $\Gamma_\nu$ is one of a certain family of congruence subgroups of $\Gamma$ with $p$ in their level. Let $\phi^0_ {\lambda,\epsilon}$ denote the map induced by $\phi_{\lambda,\epsilon}$ on the $\Gamma\pi\Gamma$-ordinary part of $H^\ast(\Gamma,\mathbb{D})$. Our main theorem states that the kernel of $\phi^0_{\lambda,\epsilon}$ is $I_{\lambda,\epsilon}H^\ast(\Gamma,\mathbb{D})^0$ where $I_{\lambda,\epsilon}$ is the kernel of the ring homomorphism induced on $\Lambda$ by the character $\lambda$ .</dc:description>
<dc:publisher lang="0">Universitat de Barcelona</dc:publisher>
<dc:date>1997</dc:date>
<dc:type>info:eu-repo/semantics/article</dc:type>
<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
<dc:format>application/pdf</dc:format>
<dc:identifier>https://www.raco.cat/index.php/CollectaneaMathematica/article/view/56362</dc:identifier>
<dc:identifier>2038-4815</dc:identifier>
<dc:source lang="ca-ES">Collectanea Mathematica; 1997: Vol.: 48 Núm.: 1 -2; p. 1-30</dc:source>
<dc:source lang="0">0010-0757</dc:source>
<dc:language>eng</dc:language>
<dc:relation>https://www.raco.cat/index.php/CollectaneaMathematica/article/view/56362/66666</dc:relation>
<dc:rights>Aquesta revista ofereix el text complet de tots els seus articles, excepte els dels cinc darrers anys, que s'aniran alliberant periòdicament fins el 2010. A partir del 2011 requereix subscripció. Podeu accedir-hi aquí. L'accés als articles a text complet inclosos a RACO és gratuït, però els actes de reproducció, distribució, comunicació pública o transformació total o parcial estan subjectes a les condicions d'ús de cada revista i poden requerir el consentiment exprés i escrit dels autors i/o institucions editores.</dc:rights>
</oai_dc:dc>
<?xml version="1.0" encoding="UTF-8" ?>
<record schemaLocation="http://www.loc.gov/MARC21/slim http://www.loc.gov/standards/marcxml/schema/MARC21slim.xsd">
<leader>naa a 5a 4500</leader>
<controlfield tag="008">AAMMDDs1997||||spc|||||s|||||0|| 0|eng|c</controlfield>
<controlfield tag="007">cr |||||||||||</controlfield>
<datafield ind1="1" ind2="0" tag="245">
<subfield code="a">$p$-adic deformations of cohomology classes of subgroups of $GL(n,\mathbb{Z})$</subfield>
<subfield code="h">[Recurs electrònic]</subfield>
</datafield>
<datafield ind1="1" ind2=" " tag="100">
<subfield code="a">Ash, Avner</subfield>
</datafield>
<datafield ind1="1" ind2=" " tag="700">
<subfield code="a">Stevens, G.</subfield>
</datafield>
<datafield ind1=" " ind2=" " tag="520">
<subfield code="a">We construct $p$-adic analytic families of $p$-ordinary cohomology classes in the cohomology of arithmetic subgroups of $GL(n)$ with coefficients in a family of representation spaces for $GL(n)$. These analytic families are parametrized by the highest weights of the coefficient modules. More precisely, we consider the cohomology of a compact $\mathbb{Z}_p$-module $\mathbb{D}$ of $p$-adic measures on a certain homogeneous space of $GL(n,\mathbb{Z}_p)$. For any dominant weight $\lambda$ with respect to a fixed choice $(B, T)$ of a Borel subgroup $B$ and a maximal split torus $T\subseteq B$ and for any finite "nebentype" character $\epsilon : T(\mathbb{Z}_p)\longrightarrow\mathbb{Z} ^x_p$ we construct a $\mathbb{Z}_p$-map from $\mathbb{D}$ to $V_{\lambda,\epsilon}$. These maps are equivariant for commuting actions of $T(\mathbb{Z}_p)$ and $\Gamma_\nu$ where $\Gamma_\nu \subseteq GL(n, \mathbb{Z})$ is a congruence subgroup analogous to $\Gamma_0(p^\nu)$ where $p^\nu$ is the conductor of $\epsilon$ . We also make the matrix $\pi := diag(1, p, p^2,\dots , p^{n-1})$ act equivariantly on all these modules. We obtain a $\Lambda := \mathbb{Z}_p[[T(\mathbb{Z}_p)]]$-module structure on $H^\ast(\Gamma,\mathbb{D})$ and Hecke actions on $H^\ast(\Gamma,\mathbb{D})$ and $H^\ast(\Gamma_\nu, V_{\lambda,\epsilon})$ with Hecke equivariant maps $\phi_{\lambda,\epsilon} : H^\ast(\Gamma,\mathbb{D})\longrightarrow H^\ast(\Gamma_\nu, V_{\lambda,\epsilon})$, where $\Gamma$ is a congruence subgroup of $GL(n,\mathbb{Z})$ of level prime to $p$ and $\Gamma_\nu$ is one of a certain family of congruence subgroups of $\Gamma$ with $p$ in their level. Let $\phi^0_ {\lambda,\epsilon}$ denote the map induced by $\phi_{\lambda,\epsilon}$ on the $\Gamma\pi\Gamma$-ordinary part of $H^\ast(\Gamma,\mathbb{D})$. Our main theorem states that the kernel of $\phi^0_{\lambda,\epsilon}$ is $I_{\lambda,\epsilon}H^\ast(\Gamma,\mathbb{D})^0$ where $I_{\lambda,\epsilon}$ is the kernel of the ring homomorphism induced on $\Lambda$ by the character $\lambda$ .</subfield>
</datafield>
<datafield ind1="4" ind2="0" tag="856">
<subfield code="z">Accés lliure</subfield>
<subfield code="u">https://www.raco.cat/index.php/CollectaneaMathematica/article/view/56362</subfield>
</datafield>
<datafield ind1="0" ind2=" " tag="730">
<subfield code="a">RACO (Articles)</subfield>
</datafield>
<datafield ind1="1" ind2=" " tag="773">
<subfield code="t">Collectanea Mathematica</subfield>
<subfield code="d">[s.l.] : Universitat de Barcelona, 1997</subfield>
<subfield code="x">2038-4815</subfield>
<subfield code="g">1997: Vol.: 48 Núm.: 1 -2, p. 1-30</subfield>
</datafield>
<datafield ind1=" " ind2="4" tag="655">
<subfield code="a">Articles de revistes electròniques</subfield>
</datafield>
</record>
<?xml version="1.0" encoding="UTF-8" ?>
<article lang="CA" schemaLocation="http://dtd.nlm.nih.gov/publishing/2.3 http://dtd.nlm.nih.gov/publishing/2.3/xsd/journalpublishing.xsd">
<front>
<journal-meta>
<journal-id journal-id-type="other">CollectaneaMathematica</journal-id>
<journal-title>Collectanea Mathematica</journal-title>
<issn pub-type="epub">2038-4815</issn>
<issn pub-type="ppub">0010-0757</issn>
<publisher>
<publisher-name>Universitat de Barcelona</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="other">56362</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Articles</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>$p$-adic deformations of cohomology classes of subgroups of $GL(n,\mathbb{Z})$</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name name-style="western">
<surname>Ash</surname>
<given-names>Avner</given-names>
</name>
</contrib>
<contrib contrib-type="author">
<name name-style="western">
<surname>Stevens</surname>
<given-names>G.</given-names>
</name>
</contrib>
<contrib contrib-type="editor">
<name>
<surname>Consorci de Biblioteques Universitaries de Catalunya</surname>
<given-names>CBUC -</given-names>
</name>
</contrib>
<contrib contrib-type="editor">
<name>
<surname>Coll</surname>
<given-names>Josep</given-names>
</name>
</contrib>
<contrib contrib-type="editor">
<name>
<surname>Exportació de revistes</surname>
<given-names>UB</given-names>
</name>
</contrib>
<contrib contrib-type="editor">
<name>
<surname>Universitat de Barcelona</surname>
<given-names>CRAI</given-names>
</name>
</contrib>
<contrib contrib-type="jmanager">
<name>
<surname>Consorci de Biblioteques Universitaries de Catalunya</surname>
<given-names>CBUC -</given-names>
</name>
</contrib>
<contrib contrib-type="jmanager">
<name>
<surname>Coll</surname>
<given-names>Josep</given-names>
</name>
</contrib>
<contrib contrib-type="jmanager">
<name>
<surname>Exportació de revistes</surname>
<given-names>UB</given-names>
</name>
</contrib>
<contrib contrib-type="jmanager">
<name>
<surname>Universitat de Barcelona</surname>
<given-names>CRAI</given-names>
</name>
</contrib>
</contrib-group>
<pub-date pub-type="epub">
<day>11</day>
<month>01</month>
<year>1997</year>
</pub-date>
<pub-date pub-type="collection">
<year>1997</year>
</pub-date>
<issue-id pub-id-type="other">4550</issue-id>
<issue-title>Vol.: 48 Núm.: 1 -2</issue-title>
<permissions>
<copyright-year>1997</copyright-year>
</permissions>
<abstract lang="CA">
<p>We construct $p$-adic analytic families of $p$-ordinary cohomology classes in the cohomology of arithmetic subgroups of $GL(n)$ with coefficients in a family of representation spaces for $GL(n)$. These analytic families are parametrized by the highest weights of the coefficient modules. More precisely, we consider the cohomology of a compact $\mathbb{Z}_p$-module $\mathbb{D}$ of $p$-adic measures on a certain homogeneous space of $GL(n,\mathbb{Z}_p)$. For any dominant weight $\lambda$ with respect to a fixed choice $(B, T)$ of a Borel subgroup $B$ and a maximal split torus $T\subseteq B$ and for any finite "nebentype" character $\epsilon : T(\mathbb{Z}_p)\longrightarrow\mathbb{Z} ^x_p$ we construct a $\mathbb{Z}_p$-map from $\mathbb{D}$ to $V_{\lambda,\epsilon}$. These maps are equivariant for commuting actions of $T(\mathbb{Z}_p)$ and $\Gamma_\nu$ where $\Gamma_\nu \subseteq GL(n, \mathbb{Z})$ is a congruence subgroup analogous to $\Gamma_0(p^\nu)$ where $p^\nu$ is the conductor of $\epsilon$ . We also make the matrix $\pi := diag(1, p, p^2,\dots , p^{n-1})$ act equivariantly on all these modules. We obtain a $\Lambda := \mathbb{Z}_p[[T(\mathbb{Z}_p)]]$-module structure on $H^\ast(\Gamma,\mathbb{D})$ and Hecke actions on $H^\ast(\Gamma,\mathbb{D})$ and $H^\ast(\Gamma_\nu, V_{\lambda,\epsilon})$ with Hecke equivariant maps $\phi_{\lambda,\epsilon} : H^\ast(\Gamma,\mathbb{D})\longrightarrow H^\ast(\Gamma_\nu, V_{\lambda,\epsilon})$, where $\Gamma$ is a congruence subgroup of $GL(n,\mathbb{Z})$ of level prime to $p$ and $\Gamma_\nu$ is one of a certain family of congruence subgroups of $\Gamma$ with $p$ in their level. Let $\phi^0_ {\lambda,\epsilon}$ denote the map induced by $\phi_{\lambda,\epsilon}$ on the $\Gamma\pi\Gamma$-ordinary part of $H^\ast(\Gamma,\mathbb{D})$. Our main theorem states that the kernel of $\phi^0_{\lambda,\epsilon}$ is $I_{\lambda,\epsilon}H^\ast(\Gamma,\mathbb{D})^0$ where $I_{\lambda,\epsilon}$ is the kernel of the ring homomorphism induced on $\Lambda$ by the character $\lambda$ .</p>
</abstract>
</article-meta>
</front>
</article>
<?xml version="1.0" encoding="UTF-8" ?>
<oai_marc catForm="u" encLvl="3" level="m" status="c" type="a" schemaLocation="http://www.openarchives.org/OAI/1.1/oai_marc http://www.openarchives.org/OAI/1.1/oai_marc.xsd">
<fixfield id="008">"970111 1997 eng "</fixfield>
<varfield i1=" " i2=" " id="042">
<subfield label="a">dc</subfield>
</varfield>
<varfield i1="0" i2="0" id="245">
<subfield label="a">$p$-adic deformations of cohomology classes of subgroups of $GL(n,\mathbb{Z})$</subfield>
</varfield>
<varfield i1=" " i2=" " id="720">
<subfield label="a">Ash, Avner</subfield>
</varfield>
<varfield i1=" " i2=" " id="720">
<subfield label="a">Stevens, G.</subfield>
</varfield>
<varfield i1=" " i2=" " id="653">
</varfield>
<varfield i1=" " i2=" " id="520">
<subfield label="a">We construct $p$-adic analytic families of $p$-ordinary cohomology classes in the cohomology of arithmetic subgroups of $GL(n)$ with coefficients in a family of representation spaces for $GL(n)$. These analytic families are parametrized by the highest weights of the coefficient modules. More precisely, we consider the cohomology of a compact $\mathbb{Z}_p$-module $\mathbb{D}$ of $p$-adic measures on a certain homogeneous space of $GL(n,\mathbb{Z}_p)$. For any dominant weight $\lambda$ with respect to a fixed choice $(B, T)$ of a Borel subgroup $B$ and a maximal split torus $T\subseteq B$ and for any finite "nebentype" character $\epsilon : T(\mathbb{Z}_p)\longrightarrow\mathbb{Z} ^x_p$ we construct a $\mathbb{Z}_p$-map from $\mathbb{D}$ to $V_{\lambda,\epsilon}$. These maps are equivariant for commuting actions of $T(\mathbb{Z}_p)$ and $\Gamma_\nu$ where $\Gamma_\nu \subseteq GL(n, \mathbb{Z})$ is a congruence subgroup analogous to $\Gamma_0(p^\nu)$ where $p^\nu$ is the conductor of $\epsilon$ . We also make the matrix $\pi := diag(1, p, p^2,\dots , p^{n-1})$ act equivariantly on all these modules. We obtain a $\Lambda := \mathbb{Z}_p[[T(\mathbb{Z}_p)]]$-module structure on $H^\ast(\Gamma,\mathbb{D})$ and Hecke actions on $H^\ast(\Gamma,\mathbb{D})$ and $H^\ast(\Gamma_\nu, V_{\lambda,\epsilon})$ with Hecke equivariant maps $\phi_{\lambda,\epsilon} : H^\ast(\Gamma,\mathbb{D})\longrightarrow H^\ast(\Gamma_\nu, V_{\lambda,\epsilon})$, where $\Gamma$ is a congruence subgroup of $GL(n,\mathbb{Z})$ of level prime to $p$ and $\Gamma_\nu$ is one of a certain family of congruence subgroups of $\Gamma$ with $p$ in their level. Let $\phi^0_ {\lambda,\epsilon}$ denote the map induced by $\phi_{\lambda,\epsilon}$ on the $\Gamma\pi\Gamma$-ordinary part of $H^\ast(\Gamma,\mathbb{D})$. Our main theorem states that the kernel of $\phi^0_{\lambda,\epsilon}$ is $I_{\lambda,\epsilon}H^\ast(\Gamma,\mathbb{D})^0$ where $I_{\lambda,\epsilon}$ is the kernel of the ring homomorphism induced on $\Lambda$ by the character $\lambda$ .</subfield>
</varfield>
<varfield i1=" " i2=" " id="260">
<subfield label="b">Universitat de Barcelona</subfield>
</varfield>
<varfield i1=" " i2=" " id="720">
</varfield>
<varfield i1=" " i2=" " id="260">
<subfield label="c">1997-01-11 00:00:00</subfield>
</varfield>
<varfield i1=" " i2="7" id="655">
</varfield>
<varfield i1=" " i2=" " id="856">
<subfield label="q">application/pdf</subfield>
</varfield>
<varfield i1="4" i2="0" id="856">
<subfield label="u">https://www.raco.cat/index.php/CollectaneaMathematica/article/view/56362</subfield>
</varfield>
<varfield i1="0" i2=" " id="786">
<subfield label="n">Collectanea Mathematica; 1997: Vol.: 48 Núm.: 1 -2</subfield>
</varfield>
<varfield i1=" " i2=" " id="546">
<subfield label="a">eng</subfield>
</varfield>
<varfield i1=" " i2=" " id="500">
</varfield>
<varfield i1=" " i2=" " id="500">
</varfield>
<varfield i1=" " i2=" " id="500">
</varfield>
<varfield i1=" " i2=" " id="540">
</varfield>
</oai_marc>
<?xml version="1.0" encoding="UTF-8" ?>
<rfc1807 schemaLocation="http://info.internet.isi.edu:80/in-notes/rfc/files/rfc1807.txt http://www.openarchives.org/OAI/1.1/rfc1807.xsd">
<bib-version>v2</bib-version>
<id>https://www.raco.cat/index.php/CollectaneaMathematica/article/view/56362</id>
<entry>2014-03-14T10:41:09Z</entry>
<organization>Collectanea Mathematica</organization>
<organization>1997: Vol.: 48 Núm.: 1 -2; 1-30</organization>
<title>$p$-adic deformations of cohomology classes of subgroups of $GL(n,\mathbb{Z})$</title>
<author>Ash, Avner</author>
<author>Stevens, G.</author>
<date>1997-01-11 00:00:00</date>
<other_access>url:https://www.raco.cat/index.php/CollectaneaMathematica/article/view/56362</other_access>
<language>eng</language>
<abstract>We construct $p$-adic analytic families of $p$-ordinary cohomology classes in the cohomology of arithmetic subgroups of $GL(n)$ with coefficients in a family of representation spaces for $GL(n)$. These analytic families are parametrized by the highest weights of the coefficient modules. More precisely, we consider the cohomology of a compact $\mathbb{Z}_p$-module $\mathbb{D}$ of $p$-adic measures on a certain homogeneous space of $GL(n,\mathbb{Z}_p)$. For any dominant weight $\lambda$ with respect to a fixed choice $(B, T)$ of a Borel subgroup $B$ and a maximal split torus $T\subseteq B$ and for any finite "nebentype" character $\epsilon : T(\mathbb{Z}_p)\longrightarrow\mathbb{Z} ^x_p$ we construct a $\mathbb{Z}_p$-map from $\mathbb{D}$ to $V_{\lambda,\epsilon}$. These maps are equivariant for commuting actions of $T(\mathbb{Z}_p)$ and $\Gamma_\nu$ where $\Gamma_\nu \subseteq GL(n, \mathbb{Z})$ is a congruence subgroup analogous to $\Gamma_0(p^\nu)$ where $p^\nu$ is the conductor of $\epsilon$ . We also make the matrix $\pi := diag(1, p, p^2,\dots , p^{n-1})$ act equivariantly on all these modules. We obtain a $\Lambda := \mathbb{Z}_p[[T(\mathbb{Z}_p)]]$-module structure on $H^\ast(\Gamma,\mathbb{D})$ and Hecke actions on $H^\ast(\Gamma,\mathbb{D})$ and $H^\ast(\Gamma_\nu, V_{\lambda,\epsilon})$ with Hecke equivariant maps $\phi_{\lambda,\epsilon} : H^\ast(\Gamma,\mathbb{D})\longrightarrow H^\ast(\Gamma_\nu, V_{\lambda,\epsilon})$, where $\Gamma$ is a congruence subgroup of $GL(n,\mathbb{Z})$ of level prime to $p$ and $\Gamma_\nu$ is one of a certain family of congruence subgroups of $\Gamma$ with $p$ in their level. Let $\phi^0_ {\lambda,\epsilon}$ denote the map induced by $\phi_{\lambda,\epsilon}$ on the $\Gamma\pi\Gamma$-ordinary part of $H^\ast(\Gamma,\mathbb{D})$. Our main theorem states that the kernel of $\phi^0_{\lambda,\epsilon}$ is $I_{\lambda,\epsilon}H^\ast(\Gamma,\mathbb{D})^0$ where $I_{\lambda,\epsilon}$ is the kernel of the ring homomorphism induced on $\Lambda$ by the character $\lambda$ .</abstract>
</rfc1807>