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The Lifted Root Number Conjecture and Iwasawa Theory

Jürgen Ritter University of Augsburg, Augsburg, Germany
Alfred Weiss University of Alberta, Edmonton, AB, Canada
Available Formats:
Electronic ISBN: 978-1-4704-0341-6
Product Code: MEMO/157/748.E
List Price: $59.00 MAA Member Price:$53.10
AMS Member Price: $35.40 Click above image for expanded view The Lifted Root Number Conjecture and Iwasawa Theory Jürgen Ritter University of Augsburg, Augsburg, Germany Alfred Weiss University of Alberta, Edmonton, AB, Canada Available Formats:  Electronic ISBN: 978-1-4704-0341-6 Product Code: MEMO/157/748.E  List Price:$59.00 MAA Member Price: $53.10 AMS Member Price:$35.40
• Book Details

Memoirs of the American Mathematical Society
Volume: 1572002; 90 pp
MSC: 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 semi-local 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 $l$
• Requests

Review Copy – for reviewers who would like to review an AMS book
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Volume: 1572002; 90 pp
MSC: 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 semi-local 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 $l$
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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