Graph Theoretic Construction of Discrete Groups over p-adic Fields

This paper is originally designed as a part of revision of the author's preprint math.AG/9908174 "P-adic Schwarzian triangle groups of Mumford type". Recently, Yves Andr'e pointed out a flaw in that preprint; more precisely, Proposition II there was not correct, and consequently, as he pointed out, some triangle groups are missing (but only in p=2,3,5). I apologize to the readers, and will release the other part soon by the original title. In this paper, we concentrate on the constructive part, but more systematically and in more general situation. More precisely, this paper presents a complete criterion for an abstract tree of groups to be realized in the context of p-adic uniformization. This criterion provides a practical way of constructing finitely generated discrete subgroups in PGL(2,K) over a p-adic field K. In the end of this paper, we will exhibit concrete examples of such construction, which in particular shows that there exist infinitely many triangle groups.Comment: 14 pages, 2 figure

Vocabularium utriusque iuris

CCBE S. XVI , A, 1803 y V, 1401Odriozola, p. 106, dice que el "Vocabularium vtriusque iuris ..." no es obra Nebrisense (pero sí que es Antonio de Nebrija el autor del "Lexicon iuris ciuilis ...")Marca tip. en port.Sign: a-z8, A-Y8Texto a dos col. y a línea tiradaTexto con apostillas marginalesTractatus de modo studendi ... editus per ... Io. Baptista de Gazalupis: p. 691-720A Res. 38/5/0

Sex- and age-related differences in the management and outcomes of chronic heart failure: an analysis of patients from the ESC HFA EORP Heart Failure Long-Term Registry

Aims: This study aimed to assess age- and sex-related differences in management and 1-year risk for all-cause mortality and hospitalization in chronic heart failure (HF) patients. Methods and results: Of 16 354 patients included in the European Society of Cardiology Heart Failure Long-Term Registry, 9428 chronic HF patients were analysed [median age: 66 years; 28.5% women; mean left ventricular ejection fraction (LVEF) 37%]. Rates of use of guideline-directed medical therapy (GDMT) were high (angiotensin-converting enzyme inhibitors/angiotensin receptor blockers, beta-blockers and mineralocorticoid receptor antagonists: 85.7%, 88.7% and 58.8%, respectively). Crude GDMT utilization rates were lower in women than in men (all differences: P\ua0 64 0.001), and GDMT use became lower with ageing in both sexes, at baseline and at 1-year follow-up. Sex was not an independent predictor of GDMT prescription; however, age >75 years was a significant predictor of GDMT underutilization. Rates of all-cause mortality were lower in women than in men (7.1% vs. 8.7%; P\ua0=\ua00.015), as were rates of all-cause hospitalization (21.9% vs. 27.3%; P\ua075 years. Conclusions: There was a decline in GDMT use with advanced age in both sexes. Sex was not an independent predictor of GDMT or adverse outcomes. However, age >75 years independently predicted lower GDMT use and higher all-cause mortality in patients with LVEF 6445%

MODULI OF p-DIVISIBLE GROUPS

We prove several results about moduli spaces of p-divisible groups such as Rapoport–Zink spaces. Our main goal is to prove that Rapoport–Zink spaces at infinite level carry a natural structure as a perfectoid space, and to give a description purely in terms of p-adic Hodge theory of these spaces. This allows us to formulate and prove duality isomorphisms between basic Rapoport–Zink spaces at infinite level in general. Moreover, we identify the image of the period morphism, reproving results of Faltings, [Fal10]. For this, we give a general classification of p-divisible groups over OC, where C is an algebraically closed complete extension of Qp, in the spirit of Riemann’s classification of complex abelian varieties. Another key ingredient is a full faithfulness result for the Dieudonne ́ module functor for p-divisible groups over semiperfect rings (i.e. rings on which the Frobenius is surjective)

El non plus ultra de el lunario, y pronóstico perpetuo, general y particular para cada reyno y provincia

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