Galois structure of S-units
Abstract Let $K/k$ be a finite Galois extension of number fields with Galois group $G,$$S$ a large$G$-stable set of primes of $K,$ and $E$ (respectively, $\boldsymbol {\mu } )$ the $G$-module of $S$-units of $K$ (respectively, roots of unity). Previous work using the Tate sequence of $E$ and the Chi...
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| Veröffentlicht in: | The Bulletin of the London Mathematical Society 2016-04, Vol.48 (2), p.251-259 |
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| container_title | The Bulletin of the London Mathematical Society |
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| creator | Pacheco, D. R. Riveros Weiss, A. |
| description | Abstract
Let $K/k$ be a finite Galois extension of number fields with Galois group $G,$$S$ a large$G$-stable set of primes of $K,$ and $E$ (respectively, $\boldsymbol {\mu } )$ the $G$-module of $S$-units of $K$ (respectively, roots of unity). Previous work using the Tate sequence of $E$ and the Chinburg class $\Omega _m$ has shown that the stable isomorphism class of $E$ is determined by the data$\Delta S,\boldsymbol {\mu }, \Omega _m,$ and a special character $\varepsilon $ of $H^2(G,{\rm Hom}(\Delta S,\boldsymbol {\mu } )).$ This paper explains how to build a $G$-module $M$ from this data that is stably isomorphic to $E\oplus {\mathbb Z} G^n,$ for some integer $n.$ |
| doi_str_mv | 10.1112/blms/bdv100 |
| format | Article |
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Let $K/k$ be a finite Galois extension of number fields with Galois group $G,$$S$ a large$G$-stable set of primes of $K,$ and $E$ (respectively, $\boldsymbol {\mu } )$ the $G$-module of $S$-units of $K$ (respectively, roots of unity). Previous work using the Tate sequence of $E$ and the Chinburg class $\Omega _m$ has shown that the stable isomorphism class of $E$ is determined by the data$\Delta S,\boldsymbol {\mu }, \Omega _m,$ and a special character $\varepsilon $ of $H^2(G,{\rm Hom}(\Delta S,\boldsymbol {\mu } )).$ This paper explains how to build a $G$-module $M$ from this data that is stably isomorphic to $E\oplus {\mathbb Z} G^n,$ for some integer $n.$</description><identifier>ISSN: 0024-6093</identifier><identifier>EISSN: 1469-2120</identifier><identifier>DOI: 10.1112/blms/bdv100</identifier><language>eng</language><publisher>Oxford University Press</publisher><ispartof>The Bulletin of the London Mathematical Society, 2016-04, Vol.48 (2), p.251-259</ispartof><rights>2016 London Mathematical Society 2016</rights><rights>2016 London Mathematical Society</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c2641-681128e78a514296f3c65c637bcabeb873446b577840d0a8396e8547fbe20b923</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1112%2Fblms%2Fbdv100$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1112%2Fblms%2Fbdv100$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,776,780,1411,27903,27904,45553,45554</link.rule.ids></links><search><creatorcontrib>Pacheco, D. R. Riveros</creatorcontrib><creatorcontrib>Weiss, A.</creatorcontrib><title>Galois structure of S-units</title><title>The Bulletin of the London Mathematical Society</title><description>Abstract
Let $K/k$ be a finite Galois extension of number fields with Galois group $G,$$S$ a large$G$-stable set of primes of $K,$ and $E$ (respectively, $\boldsymbol {\mu } )$ the $G$-module of $S$-units of $K$ (respectively, roots of unity). Previous work using the Tate sequence of $E$ and the Chinburg class $\Omega _m$ has shown that the stable isomorphism class of $E$ is determined by the data$\Delta S,\boldsymbol {\mu }, \Omega _m,$ and a special character $\varepsilon $ of $H^2(G,{\rm Hom}(\Delta S,\boldsymbol {\mu } )).$ This paper explains how to build a $G$-module $M$ from this data that is stably isomorphic to $E\oplus {\mathbb Z} G^n,$ for some integer $n.$</description><issn>0024-6093</issn><issn>1469-2120</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp9jzFPwzAUhC0EEqEwMbJkYkFu37Md2xmhglIpiKEwW7brSEEpqewE1H9PqjB3uuW7O32E3CLMEZEtXLtLC7f9QYAzkqGQJWXI4JxkAExQCSW_JFcpfQEgB4UZuVvZtmtSnvo4-H6IIe_qfEOH76ZP1-Sitm0KN_85I58vzx_LV1q9r9bLx4p6JgVSqcdrHZS2BQpWypp7WXjJlfPWBacVF0K6QiktYAtW81IGXQhVu8DAlYzPyMO062OXUgy12cdmZ-PBIJijlzl6mclrpHGif5s2HE6h5ql62wArcOzcT51u2J8c_wP_olxN</recordid><startdate>20160401</startdate><enddate>20160401</enddate><creator>Pacheco, D. R. Riveros</creator><creator>Weiss, A.</creator><general>Oxford University Press</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20160401</creationdate><title>Galois structure of S-units</title><author>Pacheco, D. R. Riveros ; Weiss, A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2641-681128e78a514296f3c65c637bcabeb873446b577840d0a8396e8547fbe20b923</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Pacheco, D. R. Riveros</creatorcontrib><creatorcontrib>Weiss, A.</creatorcontrib><collection>CrossRef</collection><jtitle>The Bulletin of the London Mathematical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Pacheco, D. R. Riveros</au><au>Weiss, A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Galois structure of S-units</atitle><jtitle>The Bulletin of the London Mathematical Society</jtitle><date>2016-04-01</date><risdate>2016</risdate><volume>48</volume><issue>2</issue><spage>251</spage><epage>259</epage><pages>251-259</pages><issn>0024-6093</issn><eissn>1469-2120</eissn><abstract>Abstract
Let $K/k$ be a finite Galois extension of number fields with Galois group $G,$$S$ a large$G$-stable set of primes of $K,$ and $E$ (respectively, $\boldsymbol {\mu } )$ the $G$-module of $S$-units of $K$ (respectively, roots of unity). Previous work using the Tate sequence of $E$ and the Chinburg class $\Omega _m$ has shown that the stable isomorphism class of $E$ is determined by the data$\Delta S,\boldsymbol {\mu }, \Omega _m,$ and a special character $\varepsilon $ of $H^2(G,{\rm Hom}(\Delta S,\boldsymbol {\mu } )).$ This paper explains how to build a $G$-module $M$ from this data that is stably isomorphic to $E\oplus {\mathbb Z} G^n,$ for some integer $n.$</abstract><pub>Oxford University Press</pub><doi>10.1112/blms/bdv100</doi><tpages>9</tpages></addata></record> |
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| source | Wiley Online Library Journals Frontfile Complete; Alma/SFX Local Collection |
| title | Galois structure of S-units |
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