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Arithmetic properties and decomposability of Jacobians

Author(s)
Park, Soohyun, S.M. Massachusetts Institute of Technology
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Massachusetts Institute of Technology. Department of Mathematics.
Advisor
Bjorn Poonen.
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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
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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.
Description
Thesis: S.M., Massachusetts Institute of Technology, Department of Mathematics, 2018.
 
Cataloged from PDF version of thesis.
 
Includes bibliographical references (pages 27-29).
 
Date issued
2018
URI
http://hdl.handle.net/1721.1/115665
Department
Massachusetts Institute of Technology. Department of Mathematics
Publisher
Massachusetts Institute of Technology
Keywords
Mathematics.

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