Publication details
On a conjecture concerning minus parts in the style of Gross
| Authors | |
|---|---|
| Year of publication | 2008 |
| Type | Article in Periodical |
| Magazine / Source | Acta Arithmetica |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | Stark units; regulators; Gross conjecture on tori |
| Description | This paper is devoted to Gross's conjecture on tori over the base field Q. We call it the Minus Conjecture, since it involves a regulator built from units in the minus part. We recall and develop its relation to a conjecture of Burns, which is now known to hold generally in the absolutely abelian setting; however in many situations it is not clear at all how one should deduce the Minus Conjecture from it. We prove a somewhat weaker statement (order of vanishing) rather generally, and we give a proof of the Minus Conjecture for some specific classes of absolutely abelian extensions K/Q, for which K^+/Q is l-elementary and ramified in at most two primes. The field K is assumed to be of the form FK^+ where F is an arbitrary imaginary quadratic field. Our methods involve a good deal of explicit calculation; among other things, we use p-adic Gamma-functions and the Gross-Koblitz formula. |
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