A generalization of a unit index of Greither

Radan Kučera

Displaying similar documents to “A generalization of a unit index of Greither”

Annihilators of the class group of a compositum of quadratic fields

Jan Herman (2013)

Archivum Mathematicum

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This paper is devoted to a construction of new annihilators of the ideal class group of a tamely ramified compositum of quadratic fields. These annihilators are produced by a modified Rubin’s machinery. The aim of this modification is to give a stronger annihilation statement for this specific type of fields.

The cyclic subfield integer index

Bart de Smit (2000)

Journal de théorie des nombres de Bordeaux

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In this note we consider the index in the ring of integers of an abelian extension of a number field $K$ of the additive subgroup generated by integers which lie in subfields that are cyclic over $K$ . This index is finite, it only depends on the Galois group and the degree of $K$ , and we give an explicit combinatorial formula for it. When generalizing to more general Dedekind domains, a correction term can be needed if there is an inseparable extension of residue fields. We identify this correction...

The work of Mazur and Wiles on cyclotomic fields

John Coates (1980-1981)

Séminaire Bourbaki

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Stickelberger elements in function fields

David R. Hayes (1985)

Compositio Mathematica

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CM-fields with all roots of unity

Kuniaki Horie (1990)

Compositio Mathematica

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Class numbers of real cyclic number fields with small conductor

John Myron Masley (1978)

Compositio Mathematica

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Class groups of abelian fields, and the main conjecture

Cornelius Greither (1992)

Annales de l'institut Fourier

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This first part of this paper gives a proof of the main conjecture of Iwasawa theory for abelian base fields, including the case $p = 2$ , by Kolyvagin’s method of Euler systems. On the way, one obtains a general result on local units modulo circular units. This is then used to deduce theorems on the order of $χ$ -parts of $p$ -class groups of abelian number fields: first for relative class groups of real fields (again including the case $p = 2$ ). As a consequence, a generalization of the Gras conjecture...