Cyclotomic Units in Zp-Extensions
نویسندگان
چکیده
منابع مشابه
Cyclotomic Units and Class Groups in Zp-extensions of real abelian fields
For a real abelian number field F and for a prime p we study the relation between the p-parts of the class groups and of the quotients of global units modulo cyclotomic units along the cyclotomic Zp-extension of F . Assuming Greenberg’s conjecture about the vanishing of the λ-invariant of the extension, a map between these groups has been constructed by several authors, and shown to be an isomo...
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Let A be the inverse limit of the p-part of the ideal class groups in a Zpextension K∞/K. Greenberg conjectures that if r is maximal, then A is pseudo-null as a module over the Iwasawa algebra Λ (that is, has codimension at least 2). We prove this conjecture in the case that K is the field of p-th roots of unity, p has index of irregularity 1, satisfies Vandiver’s conjecture, and satisfies a mi...
متن کاملCyclotomic Extensions
For any field K, a field K(ζn) where ζn is a root of unity (of order n) is called a cyclotomic extension of K. The term cyclotomic means circle-dividing, and comes from the fact that the nth roots of unity divide a circle into arcs of equal length. We will see that the extensions K(ζn)/K have abelian Galois groups and we will look in particular at cyclotomic extensions of Q and finite fields. T...
متن کاملSPINOR GENERA UNDER Zp-EXTENSIONS
Let L be a quadratic lattice over a number field F . We lift the lattice L along a Zp-extension of F and investigate the growth of the number of spinor genera in the genus of L. Let Ln be the lattice obtained from L by extending scalars to the n-th layer of the Zp-extension. We show that, under various conditions on L and F , the number of spinor genera in the genus of Ln is 2 +O(1) where η is ...
متن کاملUNRAMIFIED EXTENSIONS AND GEOMETRIC Zp-EXTENSIONS OF GLOBAL FUNCTION FIELDS
We study on finite unramified extensions of global function fields (function fields of one valuable over a finite field). We show two results. One is an extension of Perret’s result about the ideal class group problem. Another is a construction of a geometric Zp-extension which has a certain property.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1995
ISSN: 0021-8693
DOI: 10.1006/jabr.1995.1022