2026-09-19T03:29:31Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1156652022-01-13T07:54:04Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Bjorn Poonen.
Park, Soohyun, S.M. Massachusetts Institute of Technology
Massachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2018-05-23T16:29:20Z
2018-05-23T16:29:20Z
2018
2018
http://hdl.handle.net/1721.1/115665
1036985489
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.
29 pages
eng
Massachusetts Institute of Technology
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
Mathematics.
Arithmetic properties and decomposability of Jacobians
Thesis
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<Abstract>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.</Abstract>
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