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1. CJM 2009 (vol 61 pp. 1073)
On the $2$-Rank of the Hilbert Kernel of Number Fields Let $E/F$ be a quadratic extension of
number fields. In this paper, we show that the genus formula for
Hilbert kernels, proved by M. Kolster and A. Movahhedi, gives the
$2$-rank of the Hilbert kernel of $E$ provided that the $2$-primary
Hilbert kernel of $F$ is trivial. However, since the original genus
formula is not explicit enough in a very particular case, we first
develop a refinement of this formula in order to employ it in the
calculation of the $2$-rank of $E$ whenever $F$ is totally real with
trivial $2$-primary Hilbert kernel. Finally, we apply our results to
quadratic, bi-quadratic, and tri-quadratic fields which include
a complete $2$-rank formula for the family of fields
$\Q(\sqrt{2},\sqrt{\delta})$ where $\delta$ is a squarefree integer.
Categories:11R70, 19F15 |
2. CJM 2008 (vol 60 pp. 1387)
On $n$-Dimensional Steinberg Symbols The aim of this work is to provide a new approach for constructing
$n$-dimensional Steinberg symbols on discrete valuation fields from
$(n+1)$-cocycles and to study reciprocity laws on curves related to
these symbols.
Keywords:Steinberg symbols, reciprocity laws, discrete valuation field, algebraic curves Categories:19F15, 19D45, 19C09 |
3. CJM 2005 (vol 57 pp. 180)
On the Size of the Wild Set To every pair of algebraic number fields with isomorphic Witt rings
one can associate a number, called the {\it minimum number of wild
primes}. Earlier investigations have established lower bounds for this
number. In this paper an analysis is presented that expresses the
minimum number of wild primes in terms of the number of wild dyadic
primes. This formula not only gives immediate upper bounds, but can be
considered to be an exact formula for the minimum number of wild
primes.
Categories:11E12, 11E81, 19F15, 11R29 |
4. CJM 2000 (vol 52 pp. 47)
Comparison of $K$-Theory Galois Module Structure Invariants We prove that two, apparently different, class-group valued Galois
module structure invariants associated to the algebraic $K$-groups
of rings of algebraic integers coincide. This comparison result is
particularly important in making explicit calculations.
Categories:11S99, 19F15, 19F27 |