Higher Arithmetic Intersection Theory
We give a new definition of higher arithmetic Chow groups for smooth projective varieties defined over a number field, which is similar to Gillet and Soul\'e's definition of arithmetic Chow groups. We also give a compact description of the intersection theory of such groups. A consequence...
Saved in:
| Main Authors | , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
29.12.2017
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | We give a new definition of higher arithmetic Chow groups for smooth
projective varieties defined over a number field, which is similar to Gillet
and Soul\'e's definition of arithmetic Chow groups. We also give a compact
description of the intersection theory of such groups. A consequence of this
theory is the definition of a height pairing between two higher algebraic
cycles, of complementary dimensions, whose real regulator class is zero. This
description agrees with Beilinson's height pairing for the classical arithmetic
Chow groups. We also give examples of the higher arithmetic intersection
pairing in dimension zero that, assuming a conjecture by Milnor on the
independence of the values of the dilogarithm, are non zero. |
|---|---|
| AbstractList | We give a new definition of higher arithmetic Chow groups for smooth
projective varieties defined over a number field, which is similar to Gillet
and Soul\'e's definition of arithmetic Chow groups. We also give a compact
description of the intersection theory of such groups. A consequence of this
theory is the definition of a height pairing between two higher algebraic
cycles, of complementary dimensions, whose real regulator class is zero. This
description agrees with Beilinson's height pairing for the classical arithmetic
Chow groups. We also give examples of the higher arithmetic intersection
pairing in dimension zero that, assuming a conjecture by Milnor on the
independence of the values of the dilogarithm, are non zero. |
| Author | Burgos-Gil, José Ignacio Goswami, Souvik |
| Author_xml | – sequence: 1 givenname: José Ignacio surname: Burgos-Gil fullname: Burgos-Gil, José Ignacio – sequence: 2 givenname: Souvik surname: Goswami fullname: Goswami, Souvik |
| BackLink | https://doi.org/10.48550/arXiv.1712.10150$$DView paper in arXiv |
| BookMark | eNotzjsLwjAUBeAMOvj6AU52cWy9N2madBTxBYJL95LGWxuwrcQi-u99TgcOh8M3ZL2mbYixKUIUaylhYfzD3SNUyCMElDBg8507V-SDpXddVVPnbLBvOvI3sp1rmyCrqPXPMeuX5nKjyT9HLNuss9UuPBy3-9XyEJpEQUgnaxNNRDq2nISk4l2TNALAcGV4oZFDzFV6ApUg17EqS6EMSMTivU3FiM1-t19nfvWuNv6Zf7z51ytelfY7oA |
| ContentType | Journal Article |
| Copyright | http://arxiv.org/licenses/nonexclusive-distrib/1.0 |
| Copyright_xml | – notice: http://arxiv.org/licenses/nonexclusive-distrib/1.0 |
| DBID | AKZ GOX |
| DOI | 10.48550/arxiv.1712.10150 |
| DatabaseName | arXiv Mathematics arXiv.org |
| DatabaseTitleList | |
| Database_xml | – sequence: 1 dbid: GOX name: arXiv.org url: http://arxiv.org/find sourceTypes: Open Access Repository |
| DeliveryMethod | fulltext_linktorsrc |
| ExternalDocumentID | 1712_10150 |
| GroupedDBID | AKZ GOX |
| ID | FETCH-LOGICAL-a670-edcc68eee84c2e35eba67e5a300a27a2b81204279d07612847ff37a0511beba93 |
| IEDL.DBID | GOX |
| IngestDate | Mon Jan 08 05:45:14 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | false |
| IsScholarly | false |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-a670-edcc68eee84c2e35eba67e5a300a27a2b81204279d07612847ff37a0511beba93 |
| OpenAccessLink | https://arxiv.org/abs/1712.10150 |
| ParticipantIDs | arxiv_primary_1712_10150 |
| PublicationCentury | 2000 |
| PublicationDate | 2017-12-29 |
| PublicationDateYYYYMMDD | 2017-12-29 |
| PublicationDate_xml | – month: 12 year: 2017 text: 2017-12-29 day: 29 |
| PublicationDecade | 2010 |
| PublicationYear | 2017 |
| Score | 1.687644 |
| SecondaryResourceType | preprint |
| Snippet | We give a new definition of higher arithmetic Chow groups for smooth
projective varieties defined over a number field, which is similar to Gillet
and Soul\'e's... |
| SourceID | arxiv |
| SourceType | Open Access Repository |
| SubjectTerms | Mathematics - Algebraic Geometry Mathematics - K-Theory and Homology Mathematics - Number Theory |
| Title | Higher Arithmetic Intersection Theory |
| URI | https://arxiv.org/abs/1712.10150 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwdV07T8MwED6VTiyIClB5KgOMFvE5cZwRoZYKCViKlC2y47PoQIXagPj59SMIFtbzLZ-t03d3vgfAdU2InArDyNaCFdJaZjBXzIkK0bhcGht6h5-e5eK1eGzKZgTZTy-M3nyvvtJ8YLO95RXHEF-GoHwPMZRsPbw06XMyjuIa9H_1vI8ZRX9IYn4IB4N3l92l55jAiNZHcJNqKbx01b-9h6bBLObhtrEKap2l9vhjWM5ny_sFG7YTMC2r3GPrOqmISBUdkijJeDGVWuS5xkqj8cwZ9ljUNmQKAgk4j197G-DG69biBMY-wKcpZFY6ybXjVElTiA4VceucEsoEm3DiFKYRU_uRBlC0AW4b4Z79f3QO-xgoiCPD-gLG_eaTLj2B9uYq3uIOs7RwIQ |
| link.rule.ids | 228,230,783,888 |
| linkProvider | Cornell University |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Higher+Arithmetic+Intersection+Theory&rft.au=Burgos-Gil%2C+Jos%C3%A9+Ignacio&rft.au=Goswami%2C+Souvik&rft.date=2017-12-29&rft_id=info:doi/10.48550%2Farxiv.1712.10150&rft.externalDocID=1712_10150 |