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Diophantine geometry and non-abelian reciprocity laws I
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Kim, Minhyong (2017) Diophantine geometry and non-abelian reciprocity laws I. In: Elliptic Curves, Modular Forms and Iwasawa Theory [Conference in honour of the 70th birthday of John Coates], 188 pp. 311-334. ISBN 9783319450315. doi:10.1007/978-3-319-45032-2_9 ISSN 2194-1009.
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WRAP-diophantine-geometry-non-abelian-reciprocity-laws-I-Kim-2017.pdf - Accepted Version - Requires a PDF viewer. Download (975Kb) | Preview |
Official URL: http://dx.doi.org/10.1007/978-3-319-45032-2_9
Abstract
We use non-abelian fundamental groups to define a sequence of higher reciprocity maps on the adelic points of a variety over a number field satisfying certain conditions in Galois cohomology. The non-abelian reciprocity law then states that the global points are contained in the kernel of all the reciprocity maps.
| Item Type: | Conference Item (Paper) | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Arithmetical algebraic geometry, Abelian groups, Galois cohomology | ||||||
| Series Name: | Springer Proceedings in Mathematics & Statistics | ||||||
| Publisher: | Springer International Publishing | ||||||
| Place of Publication: | Cham | ||||||
| ISBN: | 9783319450315 | ||||||
| ISSN: | 2194-1009 | ||||||
| Book Title: | Elliptic Curves, Modular Forms and Iwasawa Theory | ||||||
| Editor: | Loeffler, D. and Zerbes, S. | ||||||
| Official Date: | January 2017 | ||||||
| Dates: |
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| Volume: | 188 | ||||||
| Page Range: | pp. 311-334 | ||||||
| DOI: | 10.1007/978-3-319-45032-2_9 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Reuse Statement (publisher, data, author rights): | This is a post-peer-review, pre-copyedit version of a book chapter published in Elliptic Curves, Modular Forms and Iwasawa Theory. The final authenticated version is available online at: http://dx.doi.org/10.1007/978-3-319-45032-2_9 | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Date of first compliant deposit: | 15 April 2020 | ||||||
| Date of first compliant Open Access: | 16 April 2020 | ||||||
| Conference Paper Type: | Paper | ||||||
| Title of Event: | Elliptic Curves, Modular Forms and Iwasawa Theory [Conference in honour of the 70th birthday of John Coates] | ||||||
| Type of Event: | Conference | ||||||
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