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

An adjunction formula for the Emerton-Jacquet functor

The Emerton–Jacquet functor is a tool for studying locally analytic representations of p-adic Lie groups. It provides a way to access the theory of p-adic automorphic forms. Here we give an adjunction formula for the Emerton–Jacquet functor, relating it directly to locally analytic inductions, under a strict hypothesis that we call non-critical. We also further study the relationship to socles of principal series in the non-critical setting

Detector of alpha particles and x-rays operating in ambient air in pulse counting mode or/and with gas amplification

Ionization chambers working in ambient air in current detection mode are widely used in several applications such as smoke detection, dosimetry, therapeutic beam monitoring and cetera. The aim of this work was to investigate if gaseous detectors can operate in ambient air in pulse counting mode as well as with gas amplification. . To investigate the feasibility of this method two types of open- end gaseous detectors were build and successfully tested. The first one was a single wire or multiwire cylindrical geometry detector operating in pulse mode at a gas gain of 1. The second type alpha detector was an innovative GEM-like detector with resistive electrodes operating in air in avalanche mode at high gas gains (up to 10E4). A detailed comparison between these two detectors is given as well as comparison with the commercially available alpha detectors. The main advantages of gaseous detectors operating in air in a pulse detection mode are their simplicity, low cost and high sensitivity. One of the possible applications of these new detectors is alpha particle background monitors which, due to their low cost can find wide application not only in houses, but in public areas: airports, railway station and so on

Progress in the development of a S RETGEM-based detector for an early forest fire warning system

In this paper we present a prototype of a Strip Resistive Thick GEM photosensitive gaseous detector filled with Ne and ethylferrocene vapours at a total pressure of 1 atm for an early forest fire detection system. Tests show that it is one hundred times more sensitive than the best commercial ultraviolet flame detectors and therefore, it is able to reliably detect a flame of 1.5x1.5x1.5 m3 at a distance of about 1km. An additional and unique feature of this detector is its imaging capability, which in combination with other techniques, may significantly reduce false fire alarms when operating in an automatic mode. Preliminary results conducted with air filled photosensitive gaseous detectors are also presented. The approach main advantages include both the simplicity of manufacturing and affordability of construction materials such as plastics and glues specifically reducing detector production cost. The sensitivity of these air filled detectors at certain conditions may be as high as those filled with Ne and EF. Long term test results of such sealed detectors indicate a significant progress in this direction. We believe that our detectors utilized in addition to other flame and smoke sensors will exceptionally increase the sensitivity of forest fire detection systems. Our future efforts will be focused on attempts to commercialize such detectors utilizing our aforementioned findings.Comment: Presented at the International Conference on Micropattern gaseous detectors, Crete, Greece, June 200

Moments of the critical values of families of elliptic curves, with applications

We make conjectures on the moments of the central values of the family of all elliptic curves and on the moments of the first derivative of the central values of a large family of positive rank curves. In both cases the order of magnitude is the same as that of the moments of the central values of an orthogonal family of L-functions. Notably, we predict that the critical values of all rank 1 elliptic curves is logarithmically larger than the rank 1 curves in the positive rank family. Furthermore, as arithmetical applications we make a conjecture on the distribution of a_p's amongst all rank 2 elliptic curves, and also show how the Riemann hypothesis can be deduced from sufficient knowledge of the first moment of the positive rank family (based on an idea of Iwaniec).Comment: 24 page

Performance of wire-type Rn detectors operated with gas gain in ambient air in view of its possible application to early earthquake predictions

We describe a detector of alpha particles based on wire type counters (single-wire and multiwire) operating in ambient air at high gas gains (100-1000). The main advantages of these detectors are: low cost, robustness and ability to operate in humid air. The minimum detectable activity achieved with the multiwire detector for an integration time of 1 min is 140 Bq per m3, which is comparable to that featured by commercial devices. Owing to such features the detector is suited for massive application, for example for continuous monitoring of Rn or Po contaminations or, as discussed in the paper, its use in a network of Rn counters in areas affected by earth-quakes in order to verify, on a solid statistical basis, the envisaged correlation between the sudden Rn appearance and a forthcoming earthquake

Urinary peptidomics provides a noninvasive humanized readout of diabetic nephropathy in mice

Nephropathy is among the most frequent complications of diabetes and the leading cause of end-stage renal disease. Despite the success of novel drugs in animal models, the majority of the subsequent clinical trials employing those drugs targeting diabetic nephropathy failed. This lack of translational value may in part be due to an inadequate comparability of human disease and animal models that often capture only a few aspects of disease. Here we overcome this limitation by developing a multimolecular noninvasive humanized readout of diabetic nephropathy based on urinary peptidomics. The disease-modified urinary peptides of 2 type 2 diabetic nephropathy mouse models were identified and compared with previously validated urinary peptide markers of diabetic nephropathy in humans to generate a classifier composed of 21 ortholog peptides. This classifier predicted the response to disease and treatment with inhibitors of the renin-angiotensin system in mice. The humanized classifier was significantly correlated with glomerular lesions. Using a human type 2 diabetic validation cohort of 207 patients, the classifier also distinguished between patients with and without diabetic nephropathy, and their response to renin-angiotensin system inhibition. Thus, a combination of multiple molecular features common to both human and murine disease could provide a significant change in translational drug discovery research in type 2 diabetic nephropathy

The classification of irreducible admissible mod p representations of a p-adic GL_n

Let F be a finite extension of Q_p. Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive group over \bar F_p to be supersingular. We then give the classification of irreducible admissible smooth GL_n(F)-representations over \bar F_p in terms of supersingular representations. As a consequence we deduce that supersingular is the same as supercuspidal. These results generalise the work of Barthel-Livne for n = 2. For general split reductive groups we obtain similar results under stronger hypotheses.Comment: 55 pages, to appear in Inventiones Mathematica

Resveratrol content of two Californian table grape cultivars

Research Note