The kernel of the reciprocity map of varieties over local fields
For a smooth and proper variety over a local field with residue characteristic the reciprocity map ρ : SK ) → π ) is a well-defined map from its class group to the corresponding abelianized étale fundamental group of . In this paper we show that its kernel is the direct sum of a finite group and a g...
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| Veröffentlicht in: | Journal für die reine und angewandte Mathematik 2015-01, Vol.2015 (698), p.55-69 |
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| container_issue | 698 |
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| container_title | Journal für die reine und angewandte Mathematik |
| container_volume | 2015 |
| creator | Forré, Patrick |
| description | For a smooth and proper variety
over a local field
with residue characteristic
the reciprocity map
ρ
: SK
) → π
) is a well-defined map from its class group to the corresponding abelianized étale fundamental group of
. In this paper we show that its kernel is the direct sum of a finite group and a group which is ℓ-divisible for all primes ℓ ≠
. This result generalizes the work of Shuji Saito and Uwe Jannsen for curves and surfaces to arbitrary dimensions. |
| doi_str_mv | 10.1515/crelle-2012-0122 |
| format | Article |
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over a local field
with residue characteristic
the reciprocity map
ρ
: SK
) → π
) is a well-defined map from its class group to the corresponding abelianized étale fundamental group of
. In this paper we show that its kernel is the direct sum of a finite group and a group which is ℓ-divisible for all primes ℓ ≠
. This result generalizes the work of Shuji Saito and Uwe Jannsen for curves and surfaces to arbitrary dimensions.</description><identifier>ISSN: 0075-4102</identifier><identifier>EISSN: 1435-5345</identifier><identifier>DOI: 10.1515/crelle-2012-0122</identifier><language>eng</language><publisher>De Gruyter</publisher><ispartof>Journal für die reine und angewandte Mathematik, 2015-01, Vol.2015 (698), p.55-69</ispartof><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c343t-ad4928784282c10a0e909f946836286a7415437f22545d1a1c346206fae4d9503</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.degruyter.com/document/doi/10.1515/crelle-2012-0122/pdf$$EPDF$$P50$$Gwalterdegruyter$$H</linktopdf><linktohtml>$$Uhttps://www.degruyter.com/document/doi/10.1515/crelle-2012-0122/html$$EHTML$$P50$$Gwalterdegruyter$$H</linktohtml><link.rule.ids>315,782,786,27931,27932,66761,68545</link.rule.ids></links><search><creatorcontrib>Forré, Patrick</creatorcontrib><title>The kernel of the reciprocity map of varieties over local fields</title><title>Journal für die reine und angewandte Mathematik</title><description>For a smooth and proper variety
over a local field
with residue characteristic
the reciprocity map
ρ
: SK
) → π
) is a well-defined map from its class group to the corresponding abelianized étale fundamental group of
. In this paper we show that its kernel is the direct sum of a finite group and a group which is ℓ-divisible for all primes ℓ ≠
. This result generalizes the work of Shuji Saito and Uwe Jannsen for curves and surfaces to arbitrary dimensions.</description><issn>0075-4102</issn><issn>1435-5345</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LAzEQhoMoWKt3j_kD0cnH7MfNUvyCgpd6DiE70a1ptyRbpf_eLPXqYZh3Bp5heBi7lXAnUeK9TxQjCQVSiVLqjM2k0ShQGzxnM4AahZGgLtlVzhsAQFmrGXtYfxL_orSjyIfAxzIl8v0-Db4fj3zr9tP626Wexp4yH74p8Th4F3noKXb5ml0EFzPd_PU5e396XC9fxOrt-XW5WAmvjR6F60yrmroxqlFeggNqoQ2tqRpdqaZytZFodB2UQoOddLJglYIqODJdi6DnDE53fRpyThTsPvVbl45Wgp0M2JMBOxmwk4GCLE7Ij4sjpY4-0uFYgt0Mh7Qrz_6LloBV2yDqX_KiY3c</recordid><startdate>20150101</startdate><enddate>20150101</enddate><creator>Forré, Patrick</creator><general>De Gruyter</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20150101</creationdate><title>The kernel of the reciprocity map of varieties over local fields</title><author>Forré, Patrick</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c343t-ad4928784282c10a0e909f946836286a7415437f22545d1a1c346206fae4d9503</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Forré, Patrick</creatorcontrib><collection>CrossRef</collection><jtitle>Journal für die reine und angewandte Mathematik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Forré, Patrick</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The kernel of the reciprocity map of varieties over local fields</atitle><jtitle>Journal für die reine und angewandte Mathematik</jtitle><date>2015-01-01</date><risdate>2015</risdate><volume>2015</volume><issue>698</issue><spage>55</spage><epage>69</epage><pages>55-69</pages><issn>0075-4102</issn><eissn>1435-5345</eissn><abstract>For a smooth and proper variety
over a local field
with residue characteristic
the reciprocity map
ρ
: SK
) → π
) is a well-defined map from its class group to the corresponding abelianized étale fundamental group of
. In this paper we show that its kernel is the direct sum of a finite group and a group which is ℓ-divisible for all primes ℓ ≠
. This result generalizes the work of Shuji Saito and Uwe Jannsen for curves and surfaces to arbitrary dimensions.</abstract><pub>De Gruyter</pub><doi>10.1515/crelle-2012-0122</doi><tpages>15</tpages><oa>free_for_read</oa></addata></record> |
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| identifier | ISSN: 0075-4102 |
| ispartof | Journal für die reine und angewandte Mathematik, 2015-01, Vol.2015 (698), p.55-69 |
| issn | 0075-4102 1435-5345 |
| language | eng |
| recordid | cdi_crossref_primary_10_1515_crelle_2012_0122 |
| source | De Gruyter journals |
| title | The kernel of the reciprocity map of varieties over local fields |
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