Jump sets in local fields

We show how to use the combinatorial notion of jump sets to parametrize the possible structures of the group of principal units of local fields, viewed as filtered modules. We establish a natural bijection between the set of jump sets and the orbit space of a $p$-adic group of filtered automorphisms acting on a free filtered module. This, together with a Markov process on Eisenstein polynomials, culminates into a mass-formula for unit filtrations. As a bonus the proof leads in many cases to explicit invariants of Eisenstein polynomials, yielding a link between the filtered structure of the unit group and ramification theory. Finally, with the basic theory of filtered modules developed here, we recover, with a more conceptual proof, a classification, due to Miki, of the possible sets of upper jumps of a wild character: these are all jump sets, with a set of exceptions explicitly prescribed by the jump set of the local field and the size of its residue field

Improve Your Legal Writing

Christine Pagano of Golden Gate University School of Law suggests some helpful resources for attorneys wishing to hone their drafting skills

The Issue of Unemployment Among People with Disabilities

The rate of unemployment for people with disabilities continues to rise greatly above that of people without disabilities. The issue seems to be exacerbated by employer biases and concerns which are not supported in the face of evidence. A lack of employer education on disability related subjects causes this misconception among both employers and the public as a whole. To resolve the underlying problem of miseducation, an increase in the self-identification of people with disabilities is necessary to provide researchers with data to assist in the formation of a revised curriculum

Improve Your Legal Writing

Christine Pagano of Golden Gate University School of Law suggests some helpful resources for attorneys wishing to hone their drafting skills

Doppler imaging of the young late-type star LO Pegasi (BD +22 4409) in September 2003

A Doppler image of the ZAMS late-type rapidly rotating star LO Pegasi, based on spectra acquired between 12 and 15 September 2003, is presented. The Least Square Deconvolution technique is applied to enhance the signal-to-noise ratio of the mean rotational broadened line profiles extracted from the observed spectra. In the present application, a unbroadened spectrum is used as a reference, instead of a simple line list, to improve the deconvolution technique applied to extract the mean profiles. The reconstructed image is similar to those previously obtained from observations taken in 1993 and 1998, and shows that LO Peg photospheric activity is dominated by high-latitude spots with a non-uniform polar cap. The latter seems to be a persistent feature as it has been observed since 1993 with little modifications. Small spots, observed between ~ 10 and ~ 60 degrees of latitude, appears to be different with respect to those present in the 1993 and 1998 maps.Comment: 21 pages, 10 figures, accepted by Monthly Notices of the Royal Astronomical Societ