Arithmetic properties and decomposability of Jacobians
Thesis: S.M., Massachusetts Institute of Technology, Department of Mathematics, 2018.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2018
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| Online Access: | http://hdl.handle.net/1721.1/115665 |
| _version_ | 1826216502776299520 |
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| author | Park, Soohyun, S.M. Massachusetts Institute of Technology |
| author2 | Bjorn Poonen. |
| author_facet | Bjorn Poonen. Park, Soohyun, S.M. Massachusetts Institute of Technology |
| author_sort | Park, Soohyun, S.M. Massachusetts Institute of Technology |
| collection | MIT |
| description | Thesis: S.M., Massachusetts Institute of Technology, Department of Mathematics, 2018. |
| first_indexed | 2024-09-23T16:48:44Z |
| format | Thesis |
| id | mit-1721.1/115665 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T16:48:44Z |
| publishDate | 2018 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1156652019-04-11T07:55:00Z Arithmetic properties and decomposability of Jacobians Park, Soohyun, S.M. Massachusetts Institute of Technology Bjorn Poonen. Massachusetts Institute of Technology. Department of Mathematics. Massachusetts Institute of Technology. Department of Mathematics. Mathematics. Thesis: S.M., Massachusetts Institute of Technology, Department of Mathematics, 2018. Cataloged from PDF version of thesis. Includes bibliographical references (pages 27-29). We first give an overview of methods used to study the decomposability of Jacobians of curves over the complex numbers. This involves studying the action of a finite group on an abelian variety in general. Next, we use methods for point counting properties of curves over finite fields to study the decomposability of Jacobians over number fields and finite fields. For example, we show that the genus of curves over number fields whose Jacobians are isomorphic to a product of elliptic curves satisfying certain reduction conditions is bounded and give restrictions on curves over number fields whose Jacobians are isomorphic to a product of elliptic curves. by Soohyun Park. S.M. 2018-05-23T16:29:20Z 2018-05-23T16:29:20Z 2018 2018 Thesis http://hdl.handle.net/1721.1/115665 1036985489 eng MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission. http://dspace.mit.edu/handle/1721.1/7582 29 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Park, Soohyun, S.M. Massachusetts Institute of Technology Arithmetic properties and decomposability of Jacobians |
| title | Arithmetic properties and decomposability of Jacobians |
| title_full | Arithmetic properties and decomposability of Jacobians |
| title_fullStr | Arithmetic properties and decomposability of Jacobians |
| title_full_unstemmed | Arithmetic properties and decomposability of Jacobians |
| title_short | Arithmetic properties and decomposability of Jacobians |
| title_sort | arithmetic properties and decomposability of jacobians |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/115665 |
| work_keys_str_mv | AT parksoohyunsmmassachusettsinstituteoftechnology arithmeticpropertiesanddecomposabilityofjacobians |