Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter June 16, 2009

The Minus Conjecture revisited

C. Greither and R. Kučera
From the journal


In an earlier paper we proved some results concerning Gross's conjecture on tori. This conjecture, which we call the Minus Conjecture, is closely related to a conjecture of Burns, which is now known to hold generally in the absolutely abelian setting; however Burns' conjecture does not directly imply the Minus Conjecture. The result proved in the earlier paper was concerned with imaginary absolutely abelian extensions K/ℚ of the form K = FK+, with F imaginary quadratic and K+/ℚ being tame, l-elementary and ramified at most at two primes. In the present paper we complement these results by proving the Minus Conjecture for extensions K/ℚ as above but without any restriction on the number s of ramified primes. The price we have to pay for this generality is that our proof only works if the odd prime l is large enough, more precisely if l ≧ 3(s + 1). There is one more restriction, namely . (A similar restriction was already needed in our previous paper.)

Received: 2006-12-19
Revised: 2008-04-23
Published Online: 2009-06-16
Published in Print: 2009-July

© Walter de Gruyter Berlin · New York 2009

Downloaded on 2.12.2022 from
Scroll Up Arrow