Arithmetic properties and decomposability of Jacobians
Name
1036985489-MIT.pdf
Description
Full printable version
Size
1.26 MB
Format
Adobe PDF
Checksum (MD5)
156ec22da781e52b35d59572f8534a0e
Author(s)
Park, Soohyun, S.M. Massachusetts Institute of Technology
Advisor(s)
Bjorn Poonen.
Date Issued
2018
Publisher
Massachusetts Institute of Technology
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).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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