On the distribution of the Picard ranks of the reductions of a K3 surface
We report on our results concerning the distribution of the geometric Picard ranks of K3 surfaces under reduction modulo various primes. In the situation that rk Pic S [subscript overline K] is even, we introduce a quadratic character, called the jump character, such that rk Pic S [subscript overli...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer Science and Business Media LLC
2020
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| Online Access: | https://hdl.handle.net/1721.1/128891 |
| _version_ | 1826218115205169152 |
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| author | Costa, Edgar Elsenhans, Andreas-Stephan Jahnel, Jörg Martins Dias Costa, Edgar Jose |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Costa, Edgar Elsenhans, Andreas-Stephan Jahnel, Jörg Martins Dias Costa, Edgar Jose |
| author_sort | Costa, Edgar |
| collection | MIT |
| description | We report on our results concerning the distribution of the geometric Picard ranks of K3 surfaces under reduction modulo various primes. In the situation that rk Pic S [subscript overline K] is even, we introduce a quadratic character, called the jump character, such that rk Pic S [subscript overline F][subscript > Pic S [subscript overline K] for all good primes at which the character evaluates to (-1). |
| first_indexed | 2024-09-23T17:14:24Z |
| format | Article |
| id | mit-1721.1/128891 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T17:14:24Z |
| publishDate | 2020 |
| publisher | Springer Science and Business Media LLC |
| record_format | dspace |
| spelling | mit-1721.1/1288912022-09-30T00:40:07Z On the distribution of the Picard ranks of the reductions of a K3 surface Costa, Edgar Elsenhans, Andreas-Stephan Jahnel, Jörg Martins Dias Costa, Edgar Jose Massachusetts Institute of Technology. Department of Mathematics We report on our results concerning the distribution of the geometric Picard ranks of K3 surfaces under reduction modulo various primes. In the situation that rk Pic S [subscript overline K] is even, we introduce a quadratic character, called the jump character, such that rk Pic S [subscript overline F][subscript > Pic S [subscript overline K] for all good primes at which the character evaluates to (-1). 2020-12-22T15:52:21Z 2020-12-22T15:52:21Z 2020-06 2019-09 2020-06-26T13:29:20Z Article http://purl.org/eprint/type/JournalArticle 2522-0160 2363-9555 https://hdl.handle.net/1721.1/128891 Costa, Edgar et al. "On the distribution of the Picard ranks of the reductions of a K3 surface." Research in Number Theory 6, 3 (June 2020): 27 © 2020 The Author(s) en http://dx.doi.org/10.1007/s40993-020-00204-2 Research in Number Theory Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer Science and Business Media LLC Springer International Publishing |
| spellingShingle | Costa, Edgar Elsenhans, Andreas-Stephan Jahnel, Jörg Martins Dias Costa, Edgar Jose On the distribution of the Picard ranks of the reductions of a K3 surface |
| title | On the distribution of the Picard ranks of the reductions of a K3 surface |
| title_full | On the distribution of the Picard ranks of the reductions of a K3 surface |
| title_fullStr | On the distribution of the Picard ranks of the reductions of a K3 surface |
| title_full_unstemmed | On the distribution of the Picard ranks of the reductions of a K3 surface |
| title_short | On the distribution of the Picard ranks of the reductions of a K3 surface |
| title_sort | on the distribution of the picard ranks of the reductions of a k3 surface |
| url | https://hdl.handle.net/1721.1/128891 |
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