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

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

Wide field weak lensing observations of A1835 and A2204

We present mass reconstructions from weak lensing for the galaxy clusters A1835 and A2204 over 34'x34' fields using data from the ESO/MPG Wide Field Imager. Using a background galaxy population of 22<R<25.5 we detect the gravitational shear of A1835 at 8.8 sigma significance, and obtain best-fit mass profiles of sigma_v=1233^{+66}_{-70} km/s for a singular isothermal sphere model and r_{200}=1550 h^{-1} kpc, c=2.96 for a `universal' CDM profile. Using a color-selected background galaxy population of 22<R<25.8 we detect the gravitational shear of A2204 at 7.2 sigma significance, and obtain best-fit mass profiles of sigma_v=1035^{+65}_{-71} km/s for a SIS model and r_{200}=1310 h^{-1} km/s, c=6.3 for a `universal' CDM profile. The gravitational shear at distances greater than 10' is significantly detected for both clusters. The best fit weak lensing cluster masses agree well with both X-ray and dynamical mass measurements, although the central concentration of A1835 is much lower in the weak lensing mass profile than that measured by recent Chandra results. We suggest that this lower concentration is most likely a combination of contamination of the 'background' galaxy population with cluster dwarf galaxies and the effect of a prolate or tri-axial cluster core with the major axis lying near the plane of the sky. We also detect a number of additional structures at moderate significance, some of which appear to be sub-haloes associated with the clusters.Comment: accepted to A&A, 14 pages, 13 figures, version with higher quality images can be found at http://www.uni-bonn.de/~clow

Pressure and isotope effect on the anisotropy of MgB2_{2}

We analyze the data for the pressure and boron isotope effect on the temperature dependence of the magnetization near $T_{c}$. Invoking the universal scaling relation for the magnetization at fixed magnetic field it is shown that the relative shift of $T_{c}$, induced by pressure or boron isotope exchange, mirrors essentially that of the anisotropy. This uncovers a novel generic property of anisotropic type II superconductors, inexistent in the isotropic case. For MgB$_{2}$ it implies that the renormalization of the Fermi surface topology due to pressure or isotope exchange is dominated by a mechanism controlling the anisotropy.Comment: 7 pages, 3 figure

Implications of the isotope effects on the magnetization, magnetic torque and susceptibility

We analyze the magnetization, magnetic torque and susceptibility data of La2-xSrxCu(16,18)O4 and YBa2(63,65)CuO7-x near Tc in terms of the universal 3D-XY scaling relations. It is shown that the isotope effect on Tc mirrors that on the anisotropy. Invoking the generic behavior of the anisotropy the doping dependence of the isotope effects on the critical properties, including Tc, correlation lengths and magnetic penetration depths are traced back to a change of the mobile carrier concentration.Comment: 5 pages, 3 figure

A quiet flow Ludwieg tube for study of transition in compressible boundary layers: Design and feasibility

Since Ludwieg tubes have been around for many years, and NASA has already established the feasibility of creating quiet-flow wind tunnels, the major question addressed was the cost of the proposed facility. Cost estimates were obtained for major system components, and new designs which allowed fabrication at lower cost were developed. A large fraction of the facility cost comes from the fabrication of the highly polished quiet-flow supersonic nozzle. Methods for the design of this nozzle were studied at length in an attempt to find an effective but less expensive design. Progress was sufficient to show that a quality facility can be fabricated at a reasonable cost