Even Galois Representations and the Fontaine--Mazur conjecture II

We prove, under mild hypotheses, that there are no irreducible two-dimensional_even_ Galois representations of \Gal(\Qbar/\Q) which are de Rham with distinct Hodge--Tate weights. This removes the "ordinary" hypothesis required in previous work of the author. We construct examples of irreducible two-dimensional residual representations that have no characteristic zero geometric (= de Rham) deformations.Comment: Updated to take into account suggestions of the referee; the main theorems remain unchange

Endothelin-Receptor Antagonists beyond Pulmonary Arterial Hypertension: Cancer and Fibrosis.

The endothelin axis and in particular the two endothelin receptors, ETA and ETB, are targets for therapeutic intervention in human diseases. Endothelin-receptor antagonists are in clinical use to treat pulmonary arterial hypertension and have been under clinical investigation for the treatment of several other diseases, such as systemic hypertension, cancer, vasospasm, and fibrogenic diseases. In this Perspective, we review the molecules that have been evaluated in human clinical trials for the treatment of pulmonary arterial hypertension, as well as other cardiovascular diseases, cancer, and fibrosis. We will also discuss the therapeutic consequences of receptor selectivity with regard to ETA-selective, ETB-selective, or dual ETA/ETB antagonists. We will also consider which chemical characteristics are relevant to clinical use and the properties of molecules necessary for efficacy in treating diseases against which known molecules displayed suboptimal efficacy

Oddness of residually reducible Galois representations

We show that suitable congruences between polarized automorphic forms over a CM field always produce elements in the Selmer group for exactly the ±-Asai (aka tensor induction) representation that is critical in the sense of Deligne. For this we relate the oddness of the associated polarized Galois representations (in the sense of the Bella ̈ıche-Chenevier sign being +1) to the parity condition for criticality. Under an assumption similar to Vandiver’s conjecture this also provides evidence for the Fontaine-Mazur conjecture for polarized Galois representations of any even dimension

Convergence of measures on compactifications of locally symmetric spaces

We conjecture that the set of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric space S=Γ∖G/K is compact. More precisely, given a sequence of homogeneous probability measures on S, we expect that any weak limit is homogeneous with support contained in precisely one of the boundary components (including S itself). We introduce several tools to study this conjecture and we prove it in a number of cases, including when G=SL3(R) and Γ=SL3(Z)

The subconvexity problem for \GL_{2}

Generalizing and unifying prior results, we solve the subconvexity problem for the $L$-functions of \GL_{1} and \GL_{2} automorphic representations over a fixed number field, uniformly in all aspects. A novel feature of the present method is the softness of our arguments; this is largely due to a consistent use of canonically normalized period relations, such as those supplied by the work of Waldspurger and Ichino--Ikeda.Comment: Almost final version to appear in Publ. Math IHES. References updated

Effective equidistribution and the Sato-Tate law for families of elliptic curves

Extending recent work of others, we provide effective bounds on the family of all elliptic curves and one-parameter families of elliptic curves modulo p (for p prime tending to infinity) obeying the Sato-Tate Law. We present two methods of proof. Both use the framework of Murty-Sinha; the first involves only knowledge of the moments of the Fourier coefficients of the L-functions and combinatorics, and saves a logarithm, while the second requires a Sato-Tate law. Our purpose is to illustrate how the caliber of the result depends on the error terms of the inputs and what combinatorics must be done.Comment: Version 1.1, 24 pages: corrected the interpretation of Birch's moment calculations, added to the literature review of previous results

Effect of the dual endothelin receptor antagonist bosentan on untreatable skin ulcers in a patient with diabetes: a case report

<p>Abstract</p> <p>Introduction</p> <p>Refractory skin ulcers are a major burden in patients with diabetes. Their pathogenesis is multifactorial, and data increasingly implicate endothelin as a mediator of diabetic macro- and microvasculopathy. Here we describe the first reported case of an endothelin receptor antagonist being used to successfully treat refractory skin ulcers in a patient with diabetes.</p> <p>Case presentation</p> <p>An 85-year-old Caucasian man with a 30-year history of type 2 diabetes developed multiple skin ulcerations, including a right heel ulcer. Despite appropriate treatment, the ulcer showed little improvement and the risk of amputation was high. The patient was treated with the dual endothelin receptor antagonist bosentan. After three weeks of treatment, major improvements were observed, and after 21 weeks, all ulcers had healed. No abnormalities were observed during monitoring of blood pressure, erythrocyte sedimentation rate or serum aminotransferase levels.</p> <p>Conclusion</p> <p>In patients with refractory ulceration associated with diabetes, bosentan may be of real benefit, especially in terms of amputation prevention. This case supports the proposed role for endothelin in the pathogenesis of skin ulceration in diabetes and is suggestive of a potential benefit of bosentan in this patient type. This case report is of interest to diabetologists and dermatologists.</p

Increased endothelin-1 in colorectal cancer and reduction of tumour growth by ET A receptor antagonism

Endothelin-1 (ET-1) is a vasoconstrictor peptide which stimulates proliferation in vitro in different cell types, including colorectal cancer cells. Raised ET-1 levels have been detected both on tissue specimens and in the plasma of patients with cancers. To investigate the role of ET-1 in colorectal cancer: (i) ET-1 plasma levels in patients with colorectal cancer were measured by radioimmunoassay: group 1 = controls (n = 22), group 2 = primary colorectal cancer only (n = 39), group 3 = liver metastases only (n = 26); (ii) ET-1 expression in primary colorectal cancer specimens (n =10) was determined immunohistochemically and (iii) the effect of intraportally infused antagonists to the two ET-1 receptors, ET A and ET B, on the growth of liver metastases in a rat model was assessed. ET-1 plasma levels were significantly increased in both patients with primary tumour and patients with metastases, compared to controls (P < 0.01, 3.9 ± 1.4, 4.5 ± 1.5, vs. 2.75 ± 1.37 pg/ml, respectively). Immunohistochemically, strong expression of ET-1 was found in the cytoplasm, stroma and blood vessels of cancers, unlike the normal colon where only the apical layer of the epithelium, vascular endothelial cells and surrounding stroma were positively stained. In the rat model, there was significant reduction in liver tumour weights compared to controls, following treatment with the ET A antagonist (BQ123) 30 min after the intraportal inoculation of tumour cells (P < 0.05). These results suggest ET-1 is produced by colorectal cancers and may play a role in the growth of colorectal cancer acting through ET A receptors. ET A antagonists are indicated as potential anti-cancer agents. © 2001 Cancer Research Campaign http://www.bjcancer.co

Expansion in perfect groups

Let Ga be a subgroup of GL_d(Q) generated by a finite symmetric set S. For an integer q, denote by Ga_q the subgroup of Ga consisting of the elements that project to the unit element mod q. We prove that the Cayley graphs of Ga/Ga_q with respect to the generating set S form a family of expanders when q ranges over square-free integers with large prime divisors if and only if the connected component of the Zariski-closure of Ga is perfect.Comment: 62 pages, no figures, revision based on referee's comments: new ideas are explained in more details in the introduction, typos corrected, results and proofs unchange

Renin inhibition by substituted piperidines: A novel paradigm for the inhibition of monomeric aspartic proteinases?

BackgroundThe aspartic proteinase renin catalyses the first and rate-limiting step in the conversion of angiotensinogen to the hormone angiotensin II, and therefore plays an important physiological role in the regulation of blood pressure. Numerous potent peptidomimetic inhibitors of this important drug target have been developed, but none of these compounds have progressed past clinical phase II trials. Limited oral bioavailability or excessive production costs have prevented these inhibitors from becoming new antihypertensive drugs. We were interested in developing new nonpeptidomimetic renin inhibitors.ResultsHigh-throughput screening of the Roche compound library identified a simple 3,4-disubstituted piperidine lead compound. We determined the crystal structures of recombinant human renin complexed with two representatives of this new class. Binding of these substituted piperidine derivatives is accompanied by major induced-fit adaptations around the enzyme's active site.ConclusionsThe efficient optimisation of the piperidine inhibitors was facilitated by structural analysis of the renin active site in two renin-inhibitor complexes (some of the piperidine derivatives have picomolar affinities for renin). These structural changes provide the basis for a novel paradigm for inhibition of monomeric aspartic proteinases