Marta Rodriguez

Administration Time‐Dependent Effects of Valsartan on Ambulatory Blood Pressure in Elderly Hypertensive Subjects

Previous results have indicated that valsartan administration at bed‐time, as opposed to upon wakening, improves the diurnal/nocturnal ratio of blood pressure (BP) toward a normal dipping pattern, without loss of 24 h efficacy. This ratio is characterized by a progressive decrease with aging. Accordingly, we investigated the administration time‐dependent antihypertensive efficacy of valsartan, an angiotensin blocking agent, in elderly hypertensive patients. We studied 100 elderly patients with grade 1–2 essential hypertension (34 men and 66 women), 68.2±4.9 years of age, randomly assigned to receive valsartan (160 mg/d) as a monotherapy either upon awakening or at bed‐time. BP was measured for 48 h by ambulatory monitoring, at 20 min intervals between 07∶00 to 23∶00 h and at 30 min intervals at night, before and after 3 months of therapy. Physical activity was simultaneously monitored every minute by wrist actigraphy to accurately determine the duration of sleep and wake spans to enable the accurate calculation of the diurnal and nocturnal means of BP for each subject. There was a highly significant BP reduction after 3 months of valsartan treatment (p<0.001). The reduction was slightly larger with bed‐time dosing (15.3 and 9.2 mm Hg reduction in the 24 h mean of systolic and diastolic BP, respectively) than with morning dosing (12.3 and 6.3 mm Hg reduction in the 24 h mean of systolic and diastolic BP, respectively). The diurnal/nocturnal ratio, measured as the nocturnal decline of BP relative to the diurnal mean, was unchanged in the group ingesting valsartan upon awakening (−1.0 and −0.3 for systolic and diastolic BP; p>0.195). This ratio was significantly increased (6.6 and 5.4 for systolic and diastolic BP; p<0.001) when valsartan was ingested at bed‐time. The reduction of the nocturnal mean was doubled in the group ingesting valsartan at bed‐time, as compared to the group ingesting it in the morning (p<0.001). In elderly hypertensive patients, mainly characterized by a diminished nocturnal decline in BP, bed‐time valsartan dosing is better than morning dosing since it improves efficacy during the nighttime sleep span, with the potential reduction in cardiovascular risk that has been associated with a normalized diurnal/nocturnal BP ratio.

DOSE- AND ADMINISTRATION TIME-DEPENDENT EFFECTS OF NIFEDIPINE GITS ON AMBULATORY BLOOD PRESSURE IN HYPERTENSIVE SUBJECTS

Previous chronotherapy studies have shown that the circadian pattern of blood pressure (BP) remains unchanged after either morning or evening dosing of several calcium channel blockers (CCB), including amlodipine, isradipine, verapamil, nitrendipine, and cilnidipine. This trial investigated the antihypertensive efficacy and safety profile of the slow‐release, once‐a‐day nifedipine gastrointestinal therapeutic system (GITS) formulation administered at different times with reference to the rest‐activity cycle of each participant. We studied 80 diurnally active subjects (36 men and 44 women), 52.1±10.7 yrs of age, with grade 1–2 essential hypertension, who were randomly assigned to receive nifedipine GITS (30 mg/day) as a monotherapy for eight weeks, either upon awakening in the morning or at bedtime at night. Patients with uncontrolled BP were up‐titrated to a higher dose, 60 mg/day nifedipine GITS, for an additional eight weeks. BP was measured by ambulatory monitoring every 20 min during the day and every 30 min at night for 48 consecutive hours before and after therapy with either dose. The BP reduction after eight weeks of therapy with the lower dose of 30 mg/day was slightly, but not significantly, larger with bedtime dosing. The efficacy of 60 mg/day nifedipine GITS in non‐responders to the initial 30 mg/day dose was twice as great with bedtime as compared to morning dosing. Moreover, bedtime administration of nifedipine GITS reduced the incidence of edema as an adverse event by 91%, and the total number of all adverse events by 74% as compared to morning dosing (p=0.026). Independent of the time of day of administration, a single daily dose of 30 mg/day of nifedipine GITS provides full 24 h therapeutic coverage. The dose‐dependent increased efficacy and the markedly improved safety profile of bedtime as compared to morning administration of nifedipine GITS should be taken into account when prescribing this CCB in the treatment of essential hypertension.

Infinitesimal Lifting and Jacobi Criterion for Smoothness on Formal Schemes

This a first step to develop a theory of smooth, étale, and unramified morphisms between Noetherian formal schemes. Our main tool is the complete module of differentials, which is, a coherent sheaf whenever the map of formal schemes is of pseudofinite type. Among our results, we show that these infinitesimal properties of a map of usual schemes carry over into the completion with respect to suitable closed subsets. We characterize unramifiedness by the vanishing of the module of differentials. Also we see that a smooth morphism of Noetherian formal schemes is flat and its module of differentials is locally free. The article closes with a version of Zariskis Jacobian criterion.

A functorial formalism for quasi-coherent sheaves on a geometric stack

A geometric stack is a quasi-compact and semi-separated algebraic stack. We prove that the quasi-coherent sheaves on the small flat topology, Cartesian presheaves on the underlying category, and comodules over a Hopf algebroid associated to a presentation of a geometric stack are equivalent categories. As a consequence, we show that the category of quasi-coherent sheaves on a geometric stack is a Grothendieck category. We also associate, in a 2-functorial way, to a 1-morphism of geometric stacks f : X → Y, an adjunction f ∗ ⊣ f∗ for the corresponding categories of quasi-coherent sheaves that agrees with the classical one defined for schemes. This construction is described both geometrically in terms of the small flat site and algebraically in terms of comodules over the Hopf algebroid. CONTENTS Introduction 2 1. Sheaves on ringed sites 6 2. Cartesian presheaves on affine schemes 10 3. Quasi-coherent sheaves on geometric stacks 13 4. Descent of quasi-coherent sheaves on geometric stacks 20 5. Representing quasi-coherent sheaves by comodules 25 6. Properties and functoriality of quasi-coherent sheaves 33 7. Describing functoriality via comodules 40 8. Deligne-Mumford stacks and functoriality for the étale topology 45 References 49 Date: November 24, 2014. 2000 Mathematics Subject Classification. 14A20 (primary); 14F05, 18F20 (secondary). This work has been partially supported by Spain’s MEC and E.U.’s FEDER research projects MTM2008-03465 and MTM2011-26088, together with Xunta de Galicia’s PGIDIT10PXIB207144PR and GRC2013-045 . 1 2 L. ALONSO, A. JEREMÍAS, M. PÉREZ, AND M. J. VALE INTRODUCTION The theory of quasi-coherent sheaves on algebraic stacks has suffered from an unbalanced record in the published literature. Our initial aim was to develop the basic cohomological properties of quasi-coherent sheaves on algebraic stacks. The corresponding chapters of [SP] were not available when we started to study these problems, and the literature presented some gaps. This led us to pursue a general approach to quasi-coherent sheaves with the cohomology formalism in mind. The result is this paper, that has thus a semi-expository nature. Some of the results here are accessible either on unpublished papers or references with different proofs or employing a language that, in our opinion, makes the connection with the classical literature difficult. The paper also contains some new approaches to the functoriality behaviors of quasi-coherent sheaves on algebraic stacks. The setting of this paper is to define a category of quasi-coherent sheaves through a small ringed site by mimicking the original definition given in [EGA I, (5.1.3)] with a view towards an extension of [AJPV] to stacks. As we look toward cohomological properties, we restrict to a certain class of algebraic stacks, the geometric stacks —we will discuss this choice later in the introduction. We will show that to such an algebraic stack X one can associate an abelian category of Qco(X) that is Grothendieck, i.e. cocomplete with exact filtered direct limits and possessing a generator. Moreover this category agrees trivially with the usual one when X is equivalent to a scheme. Further we explore the usual variances with respect to 1-morphisms and the corresponding 2-functorial properties. What are the differences between this approach and the previous ones already in the literature? The very notion of quasi-coherent sheaf on stacks usually does not refer to a ringed site but it is often mistook with a related notion, that of Cartesian presheaf. Both are equivalent for geometric stacks as we show. The sheaf approach suffers a major technical problem, namely, the lack of functoriality of the lisse-étale site. In [Ol], a solution is presented for the category of quasi-coherent sheaves defined in [LMB]. Unfortunately not all the results that we need are contained in this reference. We also develop a treatment in our setting of the adjoint functors f ∗ ⊣ f∗ associated to a 1-morphism f : X→Y together with its 2-functorial properties. Note the description in [Ol, 3.3] of f∗ is slightly incorrect because the 1-morphism f would have to be representable by schemes; it is easily repaired by considering the approach in [LMB] or in [LO]. We provide a full detailed construction of both functors. We give also an explicit description of these functors via Hopf algebroids (Corollary 7.7). We should mention that in the Stacks Project [SP] a construction similar to ours is made but using big flat sites. The drawback of this approach is that in order to the category of sheaves of modules over a big (ringed) site to possess a generator, it is necessary to make the choice of a universe. This construction makes the sites considered automatically functorial but one has QC-SHEAVES ON A GEOMETRIC STACK 3 to check the invariance of universe. We refrain from using Grothendieck universes by using sets and classes a la Von Neumann-Gödel-Bernays but we had to wrestle with the non functoriality of the small sites. This paper thus was developed mostly independently of [SP], that is why we refer to [LMB] for all the basic definitions on stacks. Outline of the paper. Let us explain first the reason why we assume always that the stacks we consider are quasi-compact and semi-separated, i.e. with affine diagonal morphism. These are called geometric stacks in [L]. On schemes, this condition is the one that reveals itself as indispensable to have a nice cohomological behavior. Moreover we may attach a site made of affine schemes, much as we may use a basis of affine open subsets on quasi-compact, semi-separated schemes, so it makes the theory simpler. And a third reason is that they may be represented by a purely algebraic object, a Hopf algebroid. This hypothesis allows us to give a shorter proof of the existence of a generator, without choosing either a big cardinal as in Gabber’s proof or appealing to the finite presentation of the category. This shortcut should be regarded as a consequence of our restricted setting. Notice that sometimes the hypothesis of semi-separateness has a reputation of being difficult to check. Fortunately, recent results of Hall (see [Hall1], especially Theorem D) “can also be used to show that many algebraic stacks of interest have affine diagonals”. For examples of this principle at work, see, for instance, [Hall2] and [HR]. For such a stack X we consider a certain variant of the small flat site, that we will denote by Xfppf (see 3.6). Its associated topos is not functorial, but still, it has enough functoriality properties to allow us to develop a useful formalism. Notice that it is finer than the classical lisse-étale site, but has the advantage that a presentation yields a covering for every object in the small flat topology. This allows for simpler proofs and the category of quasicoherent sheaves does not change. In the affine case there are three ways of understanding a quasi-coherent sheaf, namely, • as a sheaf of modules which locally admits a presentation, • as a cartesian presheaf1, and • as a module over the ring of global sections. These three aspects are, in some sense, present also in the global case. In this paper we show that they arise quite naturally when we consider a geometric stack. For the small flat site, cartesian presheaves of modules are sheaves (in fact, for any topology coarser than the fpqc) and moreover they are the same as quasi-coherent sheaves. This relation is described for the small flat site of an affine scheme in section 2, after establishing in section 1 the general properties of ringed sites that we will need. 1This property corresponds essentially to the fact that a localization of a module at an element of the ring may be computed as a tensor product. 4 L. ALONSO, A. JEREMÍAS, M. PÉREZ, AND M. J. VALE In section 3 we transport all the previous discussion to the setting of geometric stacks. A geometric stack may be described by a Hopf algebroid, as the stackification of its associated affine groupoid scheme. We prove in Theorem 3.12 that quasi-coherent sheaves and cartesian presheaves agree on a geometric stack. Next we develop in several steps an equivalence of categories between comodules over a Hopf algebroid and quasi-coherent sheaves on its associated geometric stack. In section 4, we see that quasi-coherent sheaves on a geometric stack correspond to descent data for quasi-coherent sheaves on an affine cover (Theorem 4.6). Once we are in the affine setting, we see that a descent datum corresponds to certain supplementary structure on its module of global sections. By an algebraic procedure, in section 5, we show that this structure can be transformed into the structure of a comodule, establishing a further equivalence of categories. All these equivalences combined provide the equivalence between quasi-coherent sheaves on the geometric stack and comodules over the Hopf algebroid (Corollary 5.9). An analogous result is due by Hovey under a different setting, as we will discuss later. An important consequence of this equivalence is that the category of quasi-coherent sheaves on a geometric stack is Grothendieck. The motivation for the results in the present paper is to have a convenient formalism for doing cohomology. So, it is crucial to have a good functoriality. We devote section 6 to this issue. Specifically, we show that a map between geometric stacks induces a pair of adjoint functors between the corresponding categories of quasi-coherent sheaves. This construction is not straightforward because, as we remarked before, there is no underlying map of topoi and the definition of the direct image has extra complications. Moreover, we show that these constructions are 2-functorial. One needs to check in addition that 2-cells induce a natural transformation between their associated functors, a feature of stacks. In section 7, we express the adjunction in a purely algebraic way. The benefit of this result is to put ourselves in the

Cronoterapia con torasemida en pacientes hipertensos: aumento de la duración y la eficacia terapéuticas con su administración a la hora de acostarse☆

Fundamento y objetivo La torasemida es un diuretico de asa utilizado con frecuencia en el tratamiento de la insuficiencia cardiaca, la insuficiencia renal y la hipertension, en funcion de resultados basados, sobre todo, en la medida clinica de la presion arterial, sin que se haya valorado la eficacia y la duracion del farmaco durante las 24 h. Por ello, hemos investigado la eficacia antihipertensiva y los efectos de la torasemida en el perfil circadiano de la presion arterial, administrada a distintas horas en funcion del ciclo de actividad y descanso. Pacientes y metodo Estudiamos a 58 pacientes hipertensos (25 varones y 33 mujeres) con una media (DE) de edad de 48,7 (11,9) anos, asignados aleatoriamente a 2 grupos de tratamiento en funcion del momento de tomar una dosis de 5 mg/dia de torasemida: a la hora de levantarse o a la hora de acostarse. La presion arterial se determino ambulatoriamente durante 48 h consecutivas antes y despues de 6 semanas de intervencion terapeutica. Resultados La eficacia de la torasemida fue mayor con la dosis nocturna (11,2 y 8,0 mmHg en la media de 24 h de la presion arterial sistolica y diastolica, respectivamente) que con la matutina (6,2 y 3,7 mmHg de presion sistolica y diastolica). El porcentaje de pacientes con presion arterial ambulatoria controlada fue el doble cuando se administro la torasemida a la hora de acostarse (54%) que cuando se la administro a la hora de levantarse (27%). La duracion de la eficacia terapeutica se mantuvo a lo largo de las 24 h solo cuando se administro la torasemida a la hora de acostarse. Con respecto al perfil de seguridad, 2 pacientes presentaron efectos secundarios (dolor abdominal, diarrea) con la toma matutina y 4 con la nocturna (nicturia). Conclusiones Una dosis de 5 mg/dia de torasemida en monoterapia reduce de forma eficaz la presion arterial cuando se administra el farmaco a la hora de acostarse. Se debe tener en cuenta las diferencias en la eficacia antihipertensiva, la duracion del efecto terapeutico y el grado de control en funcion de la hora de tomar la torasemida cuando se prescriba este diuretico de asa en el tratamiento de pacientes con hipertension arterial esencial.

On the Existence of a Compact Generator on the Derived Category of a Noetherian Formal Scheme

In this paper, we prove that for a noetherian formal scheme \(\mathfrak X\), its derived category of sheaves of modules with quasi-coherent torsion homologies \(\boldsymbol{\mathsf{D}}_\mathsf{qct}(\mathfrak X)\) is generated by a single compact object. In an Appendix we prove that the category of compact objects in \(\boldsymbol{\mathsf{D}}_\mathsf{qct}(\mathfrak X)\) is skeletally small.In this paper, we prove that for a noetherian formal scheme

On the derived category of quasi-coherent sheaves on an Adams geometric stack

\mathfrak X

Differing Administration Time-Dependent Effects of Aspirin on Blood Pressure in Dipper and Non-Dipper Hypertensives

, its derived category of sheaves of modules with quasi-coherent torsion homologies

The derived category of quasi-coherent sheaves and axiomatic stable homotopy

\boldsymbol{\mathsf{D}}_\mathsf{qct}(\mathfrak X)

P-149: Administration time-dependent effects of amlodipine on ambulatory blood pressure in patients with essential hypertension

is generated by a single compact object. In an Appendix we prove that the category of compact objects in