Electronic ISBN:  9781470403416 
Product Code:  MEMO/157/748.E 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 157; 2002; 90 ppMSC: Primary 11;
This paper concerns the relation between the Lifted Root Number Conjecture, as d introduced in [GRW2], and a new equivariant form of Iwasawa theory. At d present, a main conjecture of equivariant Iwasawa theory is formulated, and d its equivalence to the Lifted Root Number Conjecture is shown subject to the validity of a semilocal d version of the Root Number Conjecture, which itself is proved in the case of a d tame extension of real abelian fields.
ReadershipGraduate students and research mathematicians interested in number theory.

Table of Contents

Chapters

1. Introduction

2. The tripod

3. Restriction, deflation; change of maps, and variance with $S$

4. Definition of $\mho _S; \Omega _\Phi $ as a shadow of $\mho _S$

5. $\mho _S$ over the maximal order in the case when $G$ is abelian

6. Local considerations

7. Towards a representing homomorphism for $\Omega _{\varphi _\mathcal {L}}$

8. Real cyclotomic extensions tame over $l$


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This paper concerns the relation between the Lifted Root Number Conjecture, as d introduced in [GRW2], and a new equivariant form of Iwasawa theory. At d present, a main conjecture of equivariant Iwasawa theory is formulated, and d its equivalence to the Lifted Root Number Conjecture is shown subject to the validity of a semilocal d version of the Root Number Conjecture, which itself is proved in the case of a d tame extension of real abelian fields.
Graduate students and research mathematicians interested in number theory.

Chapters

1. Introduction

2. The tripod

3. Restriction, deflation; change of maps, and variance with $S$

4. Definition of $\mho _S; \Omega _\Phi $ as a shadow of $\mho _S$

5. $\mho _S$ over the maximal order in the case when $G$ is abelian

6. Local considerations

7. Towards a representing homomorphism for $\Omega _{\varphi _\mathcal {L}}$

8. Real cyclotomic extensions tame over $l$