Class fields towers of imaginary quadratic fields.
Class group of a cyclotomic -extension
Class groups and general linear group cohomology for a ring of algebraic integers.
Class groups of abelian fields, and the main conjecture
This first part of this paper gives a proof of the main conjecture of Iwasawa theory for abelian base fields, including the case , 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 -parts of -class groups of abelian number fields: first for relative class groups of real fields (again including the case ). As a consequence, a generalization of the Gras conjecture is stated...
Class groups of global fields.
Class groups of large ranks in biquadratic fields
For any integer , we provide a parametric family of biquadratic fields with class groups having -rank at least 2. Moreover, in some cases, the -rank is bigger than 4.
Class groups under relative quadratic extensions
Class number and factorization in quadratic number fields
Class number divisibility of relative quadratic function fields
Class number one problem for real quadratic fields of a certain type
Class number parity of a compositum of five quadratic fields
Class Number Two for Real Quadratic Fields of Richaud-Degert Type
2000 Mathematics Subject Classification: Primary: 11D09, 11A55, 11C08, 11R11, 11R29; Secondary: 11R65, 11S40; 11R09.This paper contains proofs of conjectures made in [16] on class number 2 and what this author has dubbed the Euler-Rabinowitsch polynomial for real quadratic fields. As well, we complete the list of Richaud-Degert types given in [16] and show how the behaviour of the Euler-Rabinowitsch polynomials and certain continued fraction expansions come into play in the complete determination...
Class Numbers and Zp-Extensions.
Class numbers of certain real abelian fields
Class numbers of cyclotomic function fields
Class numbers of quadratic fields and Shimura's correspondence.
Class numbers of real cyclic number fields with small conductor
Class numbers of real quadratic function fields
Class numbers of ring class fields of prime conductor
Class numbers of totally real fields and applications to the Weber class number problem
The determination of the class number of totally real fields of large discriminant is known to be a difficult problem. The Minkowski bound is too large to be useful, and the root discriminant of the field can be too large to be treated by Odlyzko's discriminant bounds. We describe a new technique for determining the class number of such fields, allowing us to attack the class number problem for a large class of number fields not treatable by previously known methods. We give an application to Weber's...