Arithmetic properties and decomposability of Jacobians
Author(s)Park, Soohyun, S.M. Massachusetts Institute of Technology
Massachusetts Institute of Technology. Department of Mathematics.
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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.
Thesis: S.M., Massachusetts Institute of Technology, Department of Mathematics, 2018.Cataloged from PDF version of thesis.Includes bibliographical references (pages 27-29).
DepartmentMassachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology