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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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
2018Department
Massachusetts Institute of Technology. Department of MathematicsPublisher
Massachusetts Institute of Technology
Keywords
Mathematics.