Arakelov motivic cohomology II
We show that the constructions done in part I generalize their classical counterparts: firstly, the classical Beilinson regulator is induced by the abstract Chern class map from BGL \operatorname {BGL} to the Deligne cohomology spectrum. Secondly, Arakelov motivic cohomology is a generalization of a...
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| Veröffentlicht in: | Journal of algebraic geometry 2015-10, Vol.24 (4), p.755-786 |
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| container_title | Journal of algebraic geometry |
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| creator | Scholbach, Jakob |
| description | We show that the constructions done in part I generalize their classical counterparts: firstly, the classical Beilinson regulator is induced by the abstract Chern class map from
BGL
\operatorname {BGL}
to the Deligne cohomology spectrum. Secondly, Arakelov motivic cohomology is a generalization of arithmetic
K
K
-theory and arithmetic Chow groups. For example, this implies a decomposition of higher arithmetic
K
K
-groups in its Adams eigenspaces. Finally, we give a conceptual explanation of the height pairing: it is the natural pairing of motivic homology and Arakelov motivic cohomology. |
| doi_str_mv | 10.1090/jag/647 |
| format | Article |
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BGL
\operatorname {BGL}
to the Deligne cohomology spectrum. Secondly, Arakelov motivic cohomology is a generalization of arithmetic
K
K
-theory and arithmetic Chow groups. For example, this implies a decomposition of higher arithmetic
K
K
-groups in its Adams eigenspaces. Finally, we give a conceptual explanation of the height pairing: it is the natural pairing of motivic homology and Arakelov motivic cohomology.</description><identifier>ISSN: 1056-3911</identifier><identifier>EISSN: 1534-7486</identifier><identifier>DOI: 10.1090/jag/647</identifier><language>eng</language><ispartof>Journal of algebraic geometry, 2015-10, Vol.24 (4), p.755-786</ispartof><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c225t-1a723eb931baab413dd73e8a9d9e009a3d559e0f7caabfdc1ff8421969bdcd9e3</citedby><cites>FETCH-LOGICAL-c225t-1a723eb931baab413dd73e8a9d9e009a3d559e0f7caabfdc1ff8421969bdcd9e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Scholbach, Jakob</creatorcontrib><title>Arakelov motivic cohomology II</title><title>Journal of algebraic geometry</title><description>We show that the constructions done in part I generalize their classical counterparts: firstly, the classical Beilinson regulator is induced by the abstract Chern class map from
BGL
\operatorname {BGL}
to the Deligne cohomology spectrum. Secondly, Arakelov motivic cohomology is a generalization of arithmetic
K
K
-theory and arithmetic Chow groups. For example, this implies a decomposition of higher arithmetic
K
K
-groups in its Adams eigenspaces. Finally, we give a conceptual explanation of the height pairing: it is the natural pairing of motivic homology and Arakelov motivic cohomology.</description><issn>1056-3911</issn><issn>1534-7486</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNotj01LAzEURYMoWKv4D2R2rmLz8pLJZFmK1oGCG12HTD7q1BkiSSn03xvR1T1wLxcOIffAnoBptjrY_aoV6oIsQKKgSnTtZWUmW4oa4JrclHJgjANIsSAP62y_wpROzZyO42l0jUufaU5T2p-bvr8lV9FOJdz955J8vDy_b17p7m3bb9Y76jiXRwpWcQyDRhisHQSg9wpDZ7XXgTFt0UtZKSpX6-gdxNgJDrrVg3d1g0vy-Pfrciolh2i-8zjbfDbAzK-WqVqmauEP6uI_0A</recordid><startdate>20151001</startdate><enddate>20151001</enddate><creator>Scholbach, Jakob</creator><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20151001</creationdate><title>Arakelov motivic cohomology II</title><author>Scholbach, Jakob</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c225t-1a723eb931baab413dd73e8a9d9e009a3d559e0f7caabfdc1ff8421969bdcd9e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Scholbach, Jakob</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of algebraic geometry</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Scholbach, Jakob</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Arakelov motivic cohomology II</atitle><jtitle>Journal of algebraic geometry</jtitle><date>2015-10-01</date><risdate>2015</risdate><volume>24</volume><issue>4</issue><spage>755</spage><epage>786</epage><pages>755-786</pages><issn>1056-3911</issn><eissn>1534-7486</eissn><abstract>We show that the constructions done in part I generalize their classical counterparts: firstly, the classical Beilinson regulator is induced by the abstract Chern class map from
BGL
\operatorname {BGL}
to the Deligne cohomology spectrum. Secondly, Arakelov motivic cohomology is a generalization of arithmetic
K
K
-theory and arithmetic Chow groups. For example, this implies a decomposition of higher arithmetic
K
K
-groups in its Adams eigenspaces. Finally, we give a conceptual explanation of the height pairing: it is the natural pairing of motivic homology and Arakelov motivic cohomology.</abstract><doi>10.1090/jag/647</doi><tpages>32</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Journal of algebraic geometry, 2015-10, Vol.24 (4), p.755-786 |
| issn | 1056-3911 1534-7486 |
| language | eng |
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| source | American Mathematical Society Journals; Alma/SFX Local Collection |
| title | Arakelov motivic cohomology II |
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