1,434 research outputs found
Quantum Drinfeld Modules II: Quantum Exponential and Ray Class Fields
This is the second in a series of two papers presenting a solution to Manin's
Real Multiplication program \cite{Man} in positive characteristic. If is a
quadratic and real extension of and is
the integral closure of in , we associate to each
modulus the {\it unit narrow ray class
field} : a class field containing the narrow ray class field,
whose class group contains an additional contribution coming from
. For a fundamental unit, we introduce the
associated {\it quantum Drinfeld module} of : a
generalization of Drinfeld module whose elements are multi-points.
The main theorem of the paper is that where is the Hilbert class
field of and ,
are the groups of traces of
torsion points of , .Comment: 41 page
Modular Invariant of Rank 1 Drinfeld Modules and Class Field Generation
The modular invariant of rank 1 Drinfeld modules is introduced and used to
formulate and prove an exact analog of the Weber-Fueter theorem for global
function fields. The main ingredient in the proof is a version of Shimura's
Main Theorem of Complex Multiplication for global function fields, which is
also proved here.Comment: 20 page
A probable giant planet imaged in the Beta Pictoris disk
Since the discovery of its dusty disk in 1984, Beta Pictoris has become the
prototype of young early-type planetary systems, and there are now various
indications that a massive Jovian planet is orbiting the star at ~ 10 AU.
However, no planets have been detected around this star so far. Our goal was to
investigate the close environment of Beta Pic, searching for planetary
companion(s). Deep adaptive-optics L'-band images of Beta Pic were recorded
using the NaCo instrument at the Very Large Telescope. A faint point-like
signal is detected at a projected distance of ~ 8 AU from the star, within the
North-East side of the dust disk. Various tests were made to rule out with a
good confidence level possible instrumental or atmospheric artifacts. The
probability of a foreground or background contaminant is extremely low, based
in addition on the analysis of previous deep Hubble Space Telescope images. The
object L'=11.2 apparent magnitude would indicate a typical temperature of ~1500
K and a mass of ~ 8 Jovian masses. If confirmed, it could explain the main
morphological and dynamical peculiarities of the Beta Pic system. The present
detection is unique among A-stars by the proximity of the resolved planet to
its parent star. Its closeness and location inside the Beta Pic disk suggest a
formation process by core accretion or disk instabilities rather than a
binary-like formation process.Comment: 5 pages, 3 figures, 1 table. A&A Letters, in pres
LP 714-37: A wide pair of ultracool dwarfs actually is a triple
LP 714-37 was identified by Phan-Bao et al. (2005) as one of the very few
wide pairs of very low mass (VLM) stars known to date, with a separation of 33
AU. Here we present adaptive optics imaging which resolves the secondary of the
wide pair into a tighter binary, with a projected angular separation of 0.36
arcsec, or 7 AU. The estimated spectral types of LP 714-37B and LP 714-37C are
M8.0 and M8.5. We discuss the implications of this finding for brown dwarf
formation scenarios.Comment: Accepted by ApJ Letter
The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR
A large fraction of the present-day stellar mass was formed between z=0.5 and
z~3 and our understanding of the formation mechanisms at work at these epochs
requires both high spatial and high spectral resolution: one shall
simultaneously} obtain images of objects with typical sizes as small as
1-2kpc(~0''.1), while achieving 20-50 km/s (R >= 5000) spectral resolution. The
obvious instrumental solution to adopt in order to tackle the science goal is
therefore a combination of multi-object 3D spectrograph with multi-conjugate
adaptive optics in large fields. A partial, but still competitive correction
shall be prefered, over a much wider field of view. This can be done by
estimating the turbulent volume from sets of natural guide stars, by optimizing
the correction to several and discrete small areas of few arcsec2 selected in a
large field (Nasmyth field of 25 arcmin) and by correcting up to the 6th, and
eventually, up to the 60th Zernike modes. Simulations on real extragalactic
fields, show that for most sources (>80%), the recovered resolution could reach
0".15-0".25 in the J and H bands. Detection of point-like objects is improved
by factors from 3 to >10, when compared with an instrument without adaptive
correction. The proposed instrument concept, FALCON, is equiped with deployable
mini-integral field units (IFUs), achieving spectral resolutions between R=5000
and 20000. Its multiplex capability, combined with high spatial and spectral
resolution characteristics, is a natural ground based complement to the next
generation of space telescopes.Comment: ESO Workshop Proceedings: Scientific Drivers for ESO Future VLT/VLTI
Instrumentation, 10 pages and 5 figure
Adaptive Optics for Astronomy
Adaptive Optics is a prime example of how progress in observational astronomy
can be driven by technological developments. At many observatories it is now
considered to be part of a standard instrumentation suite, enabling
ground-based telescopes to reach the diffraction limit and thus providing
spatial resolution superior to that achievable from space with current or
planned satellites. In this review we consider adaptive optics from the
astrophysical perspective. We show that adaptive optics has led to important
advances in our understanding of a multitude of astrophysical processes, and
describe how the requirements from science applications are now driving the
development of the next generation of novel adaptive optics techniques.Comment: to appear in ARA&A vol 50, 201
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