Cyclotomic units and Stickelberger ideals of global function fields
نویسندگان
چکیده
منابع مشابه
Hilbert-Speiser number fields and Stickelberger ideals
Let p be a prime number. We say that a number field F satisfies the condition (H ′ pn) when any abelian extension N/F of exponent dividing p has a normal integral basis with respect to the ring of p-integers. We also say that F satisfies (H ′ p∞) when it satisfies (H ′ pn) for all n ≥ 1. It is known that the rationals Q satisfy (H ′ p∞) for all prime numbers p. In this paper, we give a simple c...
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Let q be a prime power and let Fq be the nite eld with q elements. For each polynomial Q(T) in FqT ], one could use the Carlitz module to construct an abelian extension of Fq(T), called a Carlitz cyclotomic extension. Carlitz cyclotomic extensions play a fundamental role in the study of abelian extensions of Fq(T), similar to the role played by cyclotomic number elds for abelian extensions of Q...
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Introduction. Around 1980, Galovich and Rosen (cf. [GR1] and [GR2]) computed the index of cyclotomic units in the full group of units in a cyclotomic function field over a rational function field over a finite field. Later, Hayes [H1] and Oukhaba [O] obtained a few index formulae of the elliptic units in some special extensions of the global function fields with some restrictions on the infinit...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2003
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-03-03245-8