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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$56
Individual Members: US$33.60
Institutional Members: US$44.80
Order Code: MEMO/157/748
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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 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.

Readership

Graduate students and research mathematicians interested in number theory.

Table of Contents

  • Introduction
  • The Tripod
  • 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
  • Local considerations
  • Towards a representing homomorphism for \(\Omega_{\varphi_{\mathcal L}}\)
  • Real cyclotomic extensions tame over \(l\)
  • References
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