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The Minus Conjecture revisited.
- Source :
-
Journal für die Reine und Angewandte Mathematik . Jul2009, Vol. 2009 Issue 632, p127-142. 16p. - Publication Year :
- 2009
-
Abstract
- 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.) [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00754102
- Volume :
- 2009
- Issue :
- 632
- Database :
- Academic Search Index
- Journal :
- Journal für die Reine und Angewandte Mathematik
- Publication Type :
- Academic Journal
- Accession number :
- 47544420
- Full Text :
- https://doi.org/10.1515/CRELLE.2009.053