6,010 research outputs found

### On a Refined Stark Conjecture for Function Fields

We prove that a refinement of Stark's Conjecture formulated by Rubin is true
up to primes dividing the order of the Galois group, for finite, abelian
extensions of function fields over finite fields. We also show that in the case
of constant field extensions a statement stronger than Rubin's holds true

### Hecke characters and the $K$-theory of totally real and CM number fields

Let $F/K$ be an abelian extension of number fields with $F$ either CM or
totally real and $K$ totally real. If $F$ is CM and the Brumer-Stark conjecture
holds for $F/K$, we construct a family of $G(F/K)$--equivariant Hecke
characters for $F$ with infinite type equal to a special value of certain
$G(F/K)$--equivariant $L$-functions. Using results of Greither-Popescu on the
Brumer-Stark conjecture we construct $l$-adic imprimitive versions of these
characters, for primes $l> 2$. Further, the special values of these $l$-adic
Hecke characters are used to construct $G(F/K)$-equivariant
Stickelberger-splitting maps in the $l$-primary Quillen localization sequence
for $F$, extending the results obtained in 1990 by Banaszak for $K = \Bbb Q$.
We also apply the Stickelberger-splitting maps to construct special elements in
the $l$-primary piece $K_{2n}(F)_l$ of $K_{2n}(F)$ and analyze the Galois
module structure of the group $D(n)_l$ of divisible elements in $K_{2n}(F)_l$,
for all $n>0$. If $n$ is odd and coprime to $l$ and $F = K$ is a fairly general
totally real number field, we study the cyclicity of $D(n)_l$ in relation to
the classical conjecture of Iwasawa on class groups of cyclotomic fields and
its potential generalization to a wider class of number fields. Finally, if $F$
is CM, special values of our $l$-adic Hecke characters are used to construct
Euler systems in the odd $K$-groups with coefficients $K_{2n+1}(F, \Bbb
Z/l^k)$, for all $n>0$. These are vast generalizations of Kolyvagin's Euler
system of Gauss sums and of the $K$-theoretic Euler systems constructed in
Banaszak-Gajda when $K = \Bbb Q$.Comment: 38 page

### An Equivariant Main Conjecture in Iwasawa Theory and Applications

We construct a new class of Iwasawa modules, which are the number field
analogues of the p-adic realizations of the Picard 1-motives constructed by
Deligne in the 1970s and studied extensively from a Galois module structure
point of view in our recent work. We prove that the new Iwasawa modules are of
projective dimension 1 over the appropriate profinite group rings. In the
abelian case, we prove an Equivariant Main Conjecture, identifying the first
Fitting ideal of the Iwasawa module in question over the appropriate profinite
group ring with the principal ideal generated by a certain equivariant p-adic
L-function. This is an integral, equivariant refinement of the classical Main
Conjecture over totally real number fields proved by Wiles in 1990. Finally, we
use these results and Iwasawa co-descent to prove refinements of the
(imprimitive) Brumer-Stark Conjecture and the Coates-Sinnott Conjecture, away
from their 2-primary components, in the most general number field setting. All
of the above is achieved under the assumption that the relevant prime p is odd
and that the appropriate classical Iwasawa mu-invariants vanish (as conjectured
by Iwasawa.)Comment: 52 page

### Total income and sources of funding in public broadcasting â€“ capabilities and pre-requisites for all this acretion

The financing represents the most important issue which implies the existence of public broadcasters all over Europe and all over the world. Arrangements are different from a country to country : entirely from the state budget, part from the budget, part from radio tax, entirely tax etc. The financing system in Romania is built on three piles: from state budget, radio tax (licence fee per household) and own incomes. The percentage of this incomes is different, relatively variable, but the methods of using them are well defined.The article focuses on the analysis of the sources mentioned and possible options for increasing these sources.broadcasting, licence fee, sources,radio tax, budget

### Conditions for the confirmation of three-particle non-locality

The notion of genuine three-particle non-locality introduced by Svetlichny
\cite{Svetlichny} is discussed. Svetlichny's inequality which can distinguish
between genuine three-particle non-locality and two-particle non-locality is
analyzed by reinterpreting it as a frustrated network of correlations. Its
quantum mechanical maximum violation is derived and a situation is presented
that produces the maximum violation. It is shown that the measurements
performed in recent experiments to demonstrate GHZ entanglement
\cite{Bouwmeester}, \cite{Pan} do not allow this inequality to be violated, and
hence can not be taken as confirmation of genuine three-particle non-locality.
Modifications to the experiments that would make such a confirmation possible
are discussed.Comment: minor revisions, references adde

- â€¦