The Minus Conjecture revisited
| Authors | |
|---|---|
| Year of publication | 2009 |
| Type | Article in Periodical |
| Magazine / Source | Journal für die reine und angewandte Mathematik |
| MU Faculty or unit | |
| Citation | |
| Web | http://www.reference-global.com/doi/abs/10.1515/CRELLE.2009.053 |
| Field | General mathematics |
| Keywords | Stark units; regulators; Gross conjecture on tori |
| Description | 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>=3(s+1) and l does not divide hF. |
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