Expand all Collapse all | Results 1 - 3 of 3 |
1. 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 |
2. CJM 2000 (vol 52 pp. 833)
W-Groups under Quadratic Extensions of Fields To each field $F$ of characteristic not $2$, one can associate a
certain Galois group $\G_F$, the so-called W-group of $F$, which
carries essentially the same information as the Witt ring $W(F)$ of
$F$. In this paper we investigate the connection between $\wg$ and
$\G_{F(\sqrt{a})}$, where $F(\sqrt{a})$ is a proper quadratic
extension of $F$. We obtain a precise description in the case when
$F$ is a pythagorean formally real field and $a = -1$, and show that
the W-group of a proper field extension $K/F$ is a subgroup of the
W-group of $F$ if and only if $F$ is a formally real pythagorean field
and $K = F(\sqrt{-1})$. This theorem can be viewed as an analogue of
the classical Artin-Schreier's theorem describing fields fixed by
finite subgroups of absolute Galois groups. We also obtain precise
results in the case when $a$ is a double-rigid element in $F$. Some
of these results carry over to the general setting.
Categories:11E81, 12D15 |
3. CJM 1997 (vol 49 pp. 499)
Gorenstein Witt rings II The abstract Witt rings which are Gorenstein have been classified
when the dimension is one and the classification problem for those of
dimension zero has been reduced to the case of socle degree three. Here we
classifiy the Gorenstein Witt rings of fields with dimension zero and
socle degree three. They are of elementary type.
Categories:11E81, 13H10 |