First steps towards pp-adic Langlands functoriality

By the theory of Colmez and Fontaine, a de Rham representation of the Galois group of a local field roughly corresponds to a representation of the Weil-Deligne group equipped with an admissible filtration on the underlying vector space. Using a modification of the classical local Langlands correspondence, we associate with any pair consisting of a Weil-Deligne group representation and a type of a filtration (admissible or not) a specific locally algebraic representation of a general linear group. We advertise the conjecture that this pair comes from a de Rham representation if and only if the corresponding locally algebraic representation carries an invariant norm. In the crystalline case, the Weil-Deligne group representation is unramified and the associated locally algebraic representation can be studied using the classical Satake isomorphism. By extending the latter to a specific norm completion of the Hecke algebra, we show that the existence of an invariant norm implies that our pair, indeed, comes from a crystalline representation. We also show, by using the formalism of Tannakian categories, that this latter fact is compatible with classical unramified Langlands functoriality and therefore generalizes to arbitrary split reductive groups

Generalized Robba rings

We prove that any projective coadmissible module over the locally analytic distribution algebra of a compact $p$-adic Lie group is finitely generated. In particular, the category of coadmissible modules does not have enough projectives. In the Appendix a "generalized Robba ring" for uniform pro-$p$ groups is constructed which naturally contains the locally analytic distribution algebra as a subring. The construction uses the theory of generalized microlocalization of quasi-abelian normed algebras that is also developed there. We equip this generalized Robba ring with a self-dual locally convex topology extending the topology on the distribution algebra. This is used to show some results on coadmissible modules.Comment: with an appendix by Peter Schneider; revised; new titl

Direct Detection of Giant Close-In Planets Around the Source Stars of Caustic-Crossing Microlensing Events

We propose a direct method to detect close-in giant planets orbiting stars in the Galactic bulge. This method uses caustic-crossing binary microlensing events discovered by survey teams monitoring the bulge to measure light from a planet orbiting the source star. When the planet crosses the caustic, it is more magnified than the source star; its light is magnified by two orders of magnitude for Jupiter size planets. If the planet is a giant close to the star, it may be bright enough to make a significant deviation in the light curve of the star. Detection of this deviation requires intensive monitoring of the microlensing light curve using a 10-meter class telescope for a few hours after the caustic. This is the only method yet proposed to directly detect close-in planets around stars outside the solar neighborhood.Comment: 4 pages, 2 figures. Submitted to ApJ Letter

The z>4 Quasar Population Observed by Chandra and XMM-Newton

The current status of our Chandra and XMM-Newton project on high-redshift (z>4) quasars is briefly reviewed. We report the main results obtained in the last few years for the detected quasars, along with a few (~10%) intriguing cases where no detection has been obtained with Chandra snapshot observations.Comment: 4 pages, to appear in the proceedings of 'Multiwavelength AGN surveys' (Cozumel, December 8-12 2003), ed. R. Maiolino and R. Mujic

Surface waves in protoplanetary disks induced by outbursts: Concentric rings in scattered light

Context: Vertically hydrostatic protoplanetary disk models are based on the assumption that the main heating source, stellar irradiation, does not vary much with time. However, it is known that accreting young stars are variable sources of radiation. This is particularly evident for outbursting sources such as EX Lupi and FU Orionis stars. Aim: We investigate how such outbursts affect the vertical structure of the outer regions of the protoplanetary disk, in particular their appearance in scattered light at optical and near-infrared wavelengths. Methods: We employ the 3D FARGOCA radiation-hydrodynamics code, in polar coordinates, to compute the time-dependent behavior of the axisymmetric disk structure. The outbursting inner disk region is not included explicitly. Instead, its luminosity is added to the stellar luminosity and is thus included in the irradiation of the outer disk regions. For time snapshots of interest we insert the density structure into the RADMC-3D radiative transfer code and compute the appearance of the disk at optical/near-infrared wavelengths. Results: We find that, depending on the amplitude of the outbursts, the vertical structure of the disk can become highly dynamic, featuring circular surface waves of considerable amplitude. These "hills" and "valleys" on the disk's surface show up in the scattered light images as bright and dark concentric rings. Initially these rings are small and act as standing waves, but they subsequently lead to outward propagating waves, like the waves produced by a stone thrown into a pond. These waves continue long after the actual outburst has died out. Conclusions: We propose that some of the multi-ringed structures seen in optical/infrared images of several protoplanetary disks may have their origin in outbursts that occurred decades or centuries ago.Comment: Accepted for publication in A&A Letter

The evolution of the jet from Herbig Ae star HD 163296 from 1999 to 2011

Young A and B stars, the so-called Herbig Ae/Be stars (HAeBe), are surrounded by an active accretion disk and drive outflows. We study the jet HH 409, which is launched from the HAeBe star HD 163296, using new and archival observations from Chandra and HST/STIS. In X-rays we can show that the central source is not significantly extended. The approaching jet, but not the counter-jet, is detected in Ly alpha. In addition, there is red-shifted Ly alpha emission extended in the same direction as the jet, that is also absent in the counter-jet. We can rule out an accretion or disk-wind origin for this feature. In the optical we find the knots B and B2 in the counter-jet. Knot B has been observed previously, so we can derive its proper motion of 0.37+-0.01 arcsec/yr. Its electron density is 3000/cm^3, thus the cooling time scale is a few months only, so the knot needs to be reheated continuously. The shock speed derived from models of H alpha and forbidden emission lines (FELs) decreased from 50 km/s in 1999 to 30 km/s in 2011 because the shock front loses energy as it travels along the jet. Knot B2 is observed at a similar position in 2011 as knot B was in 1999, but shows a lower ionization fraction and higher mass loss rate, proving variations in the jet launching conditions.Comment: 14 pages, 8 figures, accepted by A&