Some remarks on conjectures about cyclotomic fields and -groups of
Masato Kurihara (1992)
Compositio Mathematica
Similarity:
Displaying similar documents to “Class groups of abelian fields, and the main conjecture”
Some remarks on conjectures about cyclotomic fields and -groups of
The work of Mazur and Wiles on cyclotomic fields
John Coates (1980-1981)
Séminaire Bourbaki
Similarity:
On Tate’s refinement for a conjecture of Gross and its generalization
Noboru Aoki (2004)
Journal de Théorie des Nombres de Bordeaux
Similarity:
We study Tate’s refinement for a conjecture of Gross on the values of abelian -function at and formulate its generalization to arbitrary cyclic extensions. We prove that our generalized conjecture is true in the case of number fields. This in particular implies that Tate’s refinement is true for any number field.
On the classgroups of imaginary abelian fields
David Solomon (1990)
Annales de l'institut Fourier
Similarity:
Let be an odd prime, an odd, -adic Dirichlet character and the cyclic imaginary extension of associated to . We define a “-part” of the Sylow -subgroup of the class group of and prove a result relating its -divisibility to that of the generalized Bernoulli number . This uses the results of Mazur and Wiles in Iwasawa theory over . The more difficult case, in which divides the order of is our chief concern. In this case the result is new and confirms an earlier conjecture...
Annihilators of the class group of a compositum of quadratic fields
Jan Herman (2013)
Archivum Mathematicum
Similarity:
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 Iwasawa invariants and the higher -groups associated to real quadratic fields.
Sumida-Takahashi, Hiroki (2005)
Experimental Mathematics
Similarity: