割圆域导论 第2版

　　Since the publication of the first edition， severalremarkable developments have taken place. The work of Thaine， Kolyvagin， andRubin has produced fairly elementary proofs of Ribet's converse of Herbrand'stheorem and of the Main Conjecture. The original proofs of both of these resultsused delicate techniques from algebraic geometry and were inaccessible to manyreaders. Also， Sinnott discovered a beautiful proof of the vanishing ofIwasawa's u-invariant that is much simpler than the one given in Chapter 7.Finally， Fermat's Last Theorem was proved by Wiles， using work of Frey， Ribet，Serre， Mazur， Langlands-Tunnell， Taylor-Wiles， and others. Although the proof，which is based on modular forms and elliptic curves， is much different from thecyclotomic approaches described in this book， several of the ingredients wereinspired by ideas from cyclotomic fields and Iwasawa theory.