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Abstract
The converse to Herbrand's theorem was first proved by Kenneth Ribet in his paper “A Modular Construction of Unramified p-Extensions of Q(μp)” (1976) using tools from modular forms and algebraic geometry. The proof uses many important techniques often found in number theory. In this thesis, I give an introduction to modular forms and algebraic geometry as well as algebraic number theory and cyclotomic fields in preparing the reader for Ribet's proof. The thesis contains Ribet's proof in the last chapter.
Details
Title
Ribet's converse to Herbrand's criterion
Author
Berg, Arthur Steven
Year
2002
ISBN
978-0-496-19683-8
Source type
Dissertation or Thesis
Language of publication
English
ProQuest document ID
305581984
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
