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The Lifted Root Number Conjecture for Small Sets of Places and an Application to CM-extensions

Andreas Nickel

出版	Logos-Verlag, 2008
主題	Mathematics / General
ISBN	38325196969783832519698
URL	http://books.google.com.hk/books?id=x29gPgAACAAJ&hl=&source=gbs_api

註釋

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.