Algebraic -theory and sums-of-squares formulas.
Capitulation for even -groups in the cyclotomic -extension.
Let be a prime number and be a number field. Since Iwasawa’s works, the behaviour of the -part of the ideal class group in the -extensions of has been well understood. Moreover, M. Grandet and J.-F. Jaulent gave a precise result about its abelian -group structure.On the other hand, the ideal class group of a number field may be identified with the torsion part of the of its ring of integers. The even -groups of rings of integers appear as higher versions of the class group. Many authors...
Class groups and general linear group cohomology for a ring of algebraic integers.
Densities of 4-ranks of K₂(𝒪)
Elementary abelian 2-primary parts of K₂𝓞 and related graphs in certain quadratic number fields
Equations for Mahler measure and isogenies
We study some functional equations between Mahler measures of genus-one curves in terms of isogenies between the curves. These equations have the potential to establish relationships between Mahler measure and especial values of -functions. These notes are based on a talk that the author gave at the “Cuartas Jornadas de Teoría de Números”, Bilbao, 2011.
K-groups and ideal class groups of number fields.
On the 2-primary part of K₂ of rings of integers in certain quadratic number fields
1. Introduction. For quadratic fields whose discriminant has few prime divisors, there are explicit formulas for the 4-rank of . For quadratic fields whose discriminant has arbitrarily many prime divisors, the formulas are less explicit. In this paper we will study fields of the form , where the primes are all congruent to 1 mod 8. We will prove a theorem conjectured by Conner and Hurrelbrink which examines under what conditions the 4-rank of is zero for such fields. In the course of proving...
Tame kernels of cyclic extensions of number fields
The indecomposable of fields
Topological -theory of the integers at the prime 2.
Topologie log-syntomique, cohomologie log-cristalline et cohomologie de Čech
Trace maps in algebraic K-theory and the Coates-Wiles homomorphism.