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تسجيل مستخدم جديدFunctoriality of the canonical fractional Galois ideal
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The fractional Galois ideal of [Victor P. Snaith, Starks conjecture and new Stickelberger phenomena, Canad. J. Math. 58 (2) (2006) 419--448] is a conjectural improvement on the higher Stickelberger ideals defined at negative integers, and is expected to provide non-trivial annihilators for higher K-groups of rings of integers of number fields. In this article, we extend the definition of the fractional Galois ideal to arbitrary (possibly infinite and non-abelian) Galois extensions of number fields under the assumption of Starks conjectures, and prove naturality properties under canonical changes of extension. We discuss applications of this to the construction of ideals in non-commutative Iwasawa algebras.
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The Stickelberger elements attached to an abelian extension of number fields conjecturally participate, under certain conditions, in annihilator relations involving higher algebraic K-groups. In [Victor P. Snaith, Starks conjecture and new Stickelber
ger phenomena, Canad. J. Math. 58 (2) (2006) 419--448], Snaith introduces canonical Galois modules hoped to appear in annihilator relations generalising and improving those involving Stickelberger elements. In this paper we study the first of these modules, corresponding to the classical Stickelberger element, and prove a connection with the Stark units in a special case.
We propose a candidate, which we call the fractional Galois ideal after Snaiths fractional ideal, for replacing the classical Stickelberger ideal associated to an abelian extension of number fields. The Stickelberger ideal can be seen as gathering in
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