Lifted Root Number Conjecture for small sets of places and an application to CM-extensions

By (author) Andreas Nickel

Extent: 102 pages

Publisher: Logos Verlag Berlin

Subjects: Technical Sciences: Computer Science, Engineering, IT, & Math

Series: Augsburger Schriften zur Mathematik, Physik und Informatik

Series volume number: 12

Language: English

Paperback (Published)

(July 2008)

ISBN: 9783832519698

5.71 x 8.27 inches

Price: $50.00

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Synopsis
Contributing Authors

In this paper we study a famous conjecture which relates the leading terms at zero of Artin L-functions attached to a finite Galois extension L/K of number fields to natural arithmetic invariants. This conjecture is called the Lifted Root Number Conjecture (LRNC) and has been introduced by K.W.Gruenberg, J.Ritter and A.Weiss; it depends on a set S of primes of L which is supposed to be sufficiently large. We formulate a LRNC for small sets S which only need to contain the archimedean primes. We apply this to CM-extensions which we require to be (almost) tame above a fixed odd prime p. In this case the conjecture naturally decomposes into a plus and a minus part, and it is the minus part for which we prove the LRNC at p for an infinite class of relatively abelian extensions. Moreover, we show that our results are closely related to the Rubin-Stark conjecture.

By (author) Andreas Nickel

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