Elementary abelian 2-primary parts of K₂𝓞 and related graphs in certain quadratic number fields
Elements of order 4 of the Hilbert kernel in 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.
Erratum “Algebraic -theory and etale cohomology”
Fonctions polylogarithmes, nombres polyzêtas et groupes pro-unipotents
Generalization of the Moore exact sequence and the wild kernel for higher K-groups
Generalized Artin-Hasse and Iwasawa formulas for the Hilbert symbol in a higher local field. II.
Groupes fondamentaux motiviques de Tate mixte
Higher regulators and Hecke L-series of imaginary quadratic fields I.
Hilbert symbols as maps of functors
Homologie du groupe linéaire et polylogarithmes
Jacobienne locale d'une courbe formelle relative
Karoubi’s relative Chern character and Beilinson’s regulator
We construct a variant of Karoubi’s relative Chern character for smooth varieties over and prove a comparison result with Beilinson’s regulator with values in Deligne-Beilinson cohomology. As a corollary we obtain a new proof of Burgos’ Theorem that for number fields Borel’s regulator is twice Beilinson’s regulator.
K-groups and ideal class groups of number fields.
-adic realization of geometric triangular motives. I. (Réalisation -adique des motifs triangulés géométriques. I.)
L-values and the Fitting ideal of the tame kernel for relative quadratic extensions
Motivic complexes of Suslin and Voevodsky
Multidimensional reciprocity laws.
On Bott-periodic algebraic K-theory.
Let K*(A;Z/ln) denote the mod-ln algebraic K-theory of a Z[1/l]-algebra A. Snaith ([14], [15], [16]) has studied Bott-periodic algebraic theory Ki(A;Z/ln)[1/βn], a localized version of K*(A;Z/ln) obtained by inverting a Bott element βn. For l an odd prime, Snaith has given a description of K*(A;Z/ln)[1/βn] using Adams maps between Moore spectra. These constructions are interesting, in particular for their connections with Lichtenbaum-Quillen conjecture [16].In this paper we obtain a description...
On Jannsen's conjecture for Hecke characters of imaginary quadratic fields.
We present a collection of results on a conjecture of Jannsen about the p-adic realizations associated to Hecke characters over an imaginary quadratic field K of class number 1.The conjecture is easy to check for Galois groups purely of local type (Section 1). In Section 2 we define the p-adic realizations associated to Hecke characters over K. We prove the conjecture under a geometric regularity condition for the imaginary quadratic field K at p, which is related to the property that a global Galois...