2,079 research outputs found
The definability criterions for convex projective polyhedral reflection groups
Following Vinberg, we find the criterions for a subgroup generated by
reflections \Gamma \subset \SL^{\pm}(n+1,\mathbb{R}) and its finite-index
subgroups to be definable over where is an integrally
closed Noetherian ring in the field . We apply the criterions for
groups generated by reflections that act cocompactly on irreducible properly
convex open subdomains of the -dimensional projective sphere. This gives a
method for constructing injective group homomorphisms from such Coxeter groups
to \SL^{\pm}(n+1,\mathbb{Z}). Finally we provide some examples of
\SL^{\pm}(n+1,\mathbb{Z})-representations of such Coxeter groups. In
particular, we consider simplicial reflection groups that are isomorphic to
hyperbolic simplicial groups and classify all the conjugacy classes of the
reflection subgroups in \SL^{\pm}(n+1,\mathbb{R}) that are definable over
. These were known by Goldman, Benoist, and so on previously.Comment: 31 pages, 8 figure
On compatibility between isogenies and polarisations of abelian varieties
We discuss the notion of polarised isogenies of abelian varieties, that is,
isogenies which are compatible with given principal polarisations. This is
motivated by problems of unlikely intersections in Shimura varieties. Our aim
is to show that certain questions about polarised isogenies can be reduced to
questions about unpolarised isogenies or vice versa.
Our main theorem concerns abelian varieties B which are isogenous to a fixed
abelian variety A. It establishes the existence of a polarised isogeny A to B
whose degree is polynomially bounded in n, if there exist both an unpolarised
isogeny A to B of degree n and a polarised isogeny A to B of unknown degree. As
a further result, we prove that given any two principally polarised abelian
varieties related by an unpolarised isogeny, there exists a polarised isogeny
between their fourth powers.
The proofs of both theorems involve calculations in the endomorphism algebras
of the abelian varieties, using the Albert classification of these endomorphism
algebras and the classification of Hermitian forms over division algebras
Building a Sample of Distant Clusters of Galaxies
Candidate clusters of galaxies drawn from the sample identified from the
moderately deep I-band data of the ESO Imaging Survey (EIS), have been used for
follow-up optical/infrared imaging and spectroscopic observations. The
observations were conducted to assess the nature of these candidates over a
large range of redshifts. Currently, 163 EIS candidates have (V-I) colors, 15
have (I-K) and 65 cluster fields have been observed spectroscopically. From a
preliminary analysis of these data, we find that > 65% of the candidates
studied show strong evidence of being real physical associations, over the
redshift range 0.2<z<1.1. The evidence in some cases comes directly from
spectroscopic measurements, in others indirectly from the detection of
overdensities of objects with either the same color or the same photometric
redshift, or from a combination of color and spectroscopic information.
Preliminary results also suggest that the redshift derived from the
matched-filter algorithm is a reasonable measure of the cluster's redshift,
possibly overestimating it by Delta z ~0.1, at least for systems at z<0.7.
Overdensities of red objects have been detected in over 100 candidates, 38 of
which with estimated redshifts >0.6, and six candidates in the interval
0.45<z<0.81 have either been identified directly from measured redshifts or
have been confirmed by the measurement of at least one redshift for galaxies
located along a red-sequence typical of cluster early-type galaxies. Lastly,
five candidates among those already observed in the infrared have (I-Ks) colors
consistent with them being in the redshift interval 0.8<z<1.1. The sample of
"confirmed" clusters, already the largest of its kind in the southern
hemisphere, will be further enlarged by ongoing observations.Comment: To appear in "Large Scale Structure in the X-ray Universe", ed. M.
Plionis and I. Georgantopoulos (Paris: Editions Frontieres), in pres
Spectroscopic confirmation of clusters from the ESO imaging survey
We measure redshifts for 67 galaxies in the field of six cluster candidates
from the ESO Imaging Survey (EIS). The cluster candidates are selected in the
EIS patches C and D among those with estimated mean redshifts between 0.5 and
0.7. The observations were made with EFOSC2 at the 3.6m ESO telescope.
In the six candidate cluster fields, we identify 19 possible sets of 2 to 7
galaxies in redshift space. In order to establish which of the 19 sets are
likely to correspond to real dense systems we compare our counts with those
expected from a uniform distribution of galaxies with given luminosity
function. In order to take into account the effect of the Large Scale
Structure, we modulate the probability computed from the luminosity function
with random samplings of the Canada-France Redshift Survey.
We find that four out of six candidate EIS clusters are likely to correspond
to real systems in redshift space (> 95 % confidence level). Two of these
systems have mean redshift in agreement with the redshift estimate given by the
matched filter algorithm. The other two systems have significantly lower
redshifts.
We discuss the implications of our results in the context of our ongoing
research projects aimed at defining high-redshift optically-selected cluster
samples.Comment: To appear in A&A, main journal -- 12 pages, 9 figure
ESO Imaging Survey VII. Distant Cluster Candidates over 12 square degrees
In this paper the list of candidate clusters identified from the I-band data
of the ESO Imaging Survey (EIS) is completed using the images obtained over a
total area of about 12 square degrees. Together with the data reported earlier
the total I-band coverage of EIS is 17 square degrees, which has yielded a
sample of 252 cluster candidates in the redshift range 0.2 \lsim z \lsim 1.3.
This is the largest optically-selected sample currently available in the
Southern Hemisphere. It is also well distributed in the sky thus providing
targets for a variety of VLT programs nearly year round.Comment: 5 pages, 3 figures, submitted to Astronomy & Astrophysic
A2163: Merger events in the hottest Abell galaxy cluster II. Subcluster accretion with galaxy-gas separation
Located at z = 0.203, A2163 is a rich galaxy cluster with an intra-cluster
medium (ICM) that exhibits extraordinary properties, including an exceptionally
high X-ray luminosity, average temperature, and a powerful and extended radio
halo. The irregular and complex morphology of its gas and galaxy structure
suggests that this cluster has recently undergone major merger events that
involve two or more cluster components. In this paper, we study the gas
structure and dynamics by means of spectral-imaging analysis of X-ray data
obtained from XMM-Newton and Chandra observations. From the evidence of a cold
front, we infer the westward motion of a cool core across the E-W elongated
atmosphere of the main cluster A2163-A. Located close to a galaxy over-density,
this gas 'bullet' appears to have been spatially separated from its galaxy (and
presumably dark matter component) as a result of high-velocity accretion.
From gas brightness and temperature profile analysis performed in two
opposite regions of the main cluster, we show that the ICM has been
adiabatically compressed behind the crossing 'bullet' possibly because of shock
heating, leading to a strong departure of the ICM from hydrostatic equilibrium
in this region. Assuming that the mass estimated from the Yx proxy best
indicates the overall mass of the system and that the western cluster sector is
in approximate hydrostatic equilibrium before subcluster accretion, we infer a
merger scenario between two subunits of mass ratio 1:4, leading to a present
total system mass of M500 . The exceptional
properties of A2163 present various similarities with those of 1E0657-56, the
so-called 'bullet-cluster'. These similarities are likely to be related to a
comparable merger scenario.Comment: A&A, in pres
On the Nature of the EIS Candidate Clusters: Confirmation of z<0.6 candidates
We use public V-band imaging data from the wide-angle surveys conducted by
the ESO Imaging Survey project (EIS) to further investigate the nature of the
EIS galaxy cluster candidates. These were originally identified by applying a
matched-filter algorithm which used positional and photometric data of the
galaxy sample extracted from the I-band survey images. In this paper, we apply
the same technique to the galaxy sample extracted from V-band data and compare
the new cluster detections with the original ones. We find that ~75% of the
low-redshift cluster candidates (z<0.6) are detected in both passbands and
their estimated redshifts show good agreement with the scatter in the redshift
differences being consistent with the estimated errors of the method. For the
``robust'' I-band detections the matching frequency approaches ~85%. We also
use the available (V-I) color to search for the red sequence of early-type
galaxies observed in rich clusters over a broad range of redshifts. This is
done by searching for a simultaneous overdensity in the three-dimensional
color-projected distance space. We find significant overdensities for ~75% of
the ``robust'' candidates with z_I<0.6. We find good agreement between the
characteristic color associated to the detected "red sequence" and that
predicted by passive evolution galaxy models for ellipticals at the redshift
estimated by the matched-filter. The results presented in this paper show the
usefulness of color data, even of two-band data, to both tentatively confirm
cluster candidates and to select possible cluster members for spectroscopic
observations. Based on the present results, we estimate that ~150 EIS clusters
with z_I<0.6 are real, making it one of the largest samples of galaxy clusters
in this redshift range currently available in the southern hemisphere.Comment: 11 pages, 10 figures, accepted for publication in A&
The First VLT FORS1 spectra of Lyman-break candidates in the HDF-S and AXAF Deep Field
We report on low-resolution multi-object spectroscopy of 30 faint targets (R
\~ 24-25) in the HDF-S and AXAF deep field obtained with the VLT Focal
Reducer/low dispersion Spectrograph (FORS1). Eight high-redshift galaxies with
2.75< z < 4 have been identified. The spectroscopic redshifts are in good
agreement with the photometric ones with a dispersion at z<2
and at z>2. The inferred star formation rates of the
individual objects are moderate, ranging from a few to a few tens solar masses
per year. Five out of the eight high-z objects do not show prominent emission
lines. One object has a spectrum typical of an AGN. In the AXAF field two
relatively close pairs of galaxies have been identified, with separations of
8.7 and 3.1 proper Mpc and mean redshifts of 3.11 and 3.93, respectively.Comment: 5 pages Latex, with 2 PostScript figures. Astronomy and Astrophysics,
in pres
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