The Lichtenbaum conjecture for abelian extension of imaginary quadratic fields
In this paper, we prove the cohomological Lichtenbaum conjecture of abelian extensions of imaginary quadratic fields up to a finite set of bad primes.
math.NT↗
arXiv subjects
Chaochao Sun
Publications and source records attributed to Chaochao Sun.
The Bloch groups and special values of Dedekind zeta functions
In this paper, we compare the two definitions of Bloch group, and survey the elements in Bloch group. We confirm the Lichtenbaum conjecture on the field $Q(ζ_p)$ under the assumption the truth of the base of the Bloch group of $Q(ζ_p)$ and the relations of $K_2$ group. We also study the Lichtenbaum conjecture on non-Galois fields. By PARI, we get some equations of the zeta functions on special values and the structure of tame kernel of these fields.
math.NT↗
ON cyclotomic elements and cyclotomic subgroups in K_{2} of a field
The problem of expressing an element of K_2(F) in a more explicit form gives rise to many works. To avoid a restrictive condition in a work of Tate, Browkin considered cyclotomic elements as the candidate for the element with an explicit form. In this paper, we modify and change Browkin's conjecture about cyclotomic elements into more precise forms, in particular we introduce the conception of cyclotomic subgroup. In the rational function field cases, we determine completely the exact numbers of cyclotomic elements and cyclotomic subgroups contained in a subgroup generated by finitely many different cyclotomic elements, while in the number field cases, using Faltings' theorem on Mordell conjecture we prove that there exist subgroups generated by an infinite number of cyclotomic elements to the power of some prime, which contain no nontrivial cyclotomic elements.
math.KT↗