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The Lifted Root Number Conjecture and Iwasawa Theory
Jürgen Ritter, University of Augsburg, Germany, and Alfred Weiss, University of Alberta, Edmonton, AB, Canada
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Memoirs of the American Mathematical Society
2002; 90 pp; softcover
Volume: 157
ISBN-10: 0-8218-2928-9
ISBN-13: 978-0-8218-2928-8
List Price: US$59 Individual Members: US$35.40
Institutional Members: US\$47.20
Order Code: MEMO/157/748

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.

• Restriction, deflation; change of maps, and variance with $$S$$
• Definition of $$\mho_S$$; $$\Omega_\Phi$$ as a shadow of $$\mho_S$$
• $$\mho_S$$ over the maximal order in the case when $$G$$is abelian
• Towards a representing homomorphism for $$\Omega_{\varphi_{\mathcal L}}$$
• Real cyclotomic extensions tame over $$l$$