Semipurity of tempered Deligne cohomology

In this paper we define the formal and tempered Deligne cohomology groups, that are obtained by applying the Deligne complex functor to the complexes of formal differential forms and tempered currents respectively. We then prove the existence of a duality between them, a vanishing theorem for the former and a semipurity property for the latter. The motivation of these results comes from the study of covariant arithmetic Chow groups. The semi-purity property of tempered Deligne cohomology implies, in particular, that several definitions of covariant arithmetic Chow groups agree for projective arithmetic varieties

Chern-Weil and Hilbert-Samuel formulae for singular Hermitian line bundles

We show a Chern-Weil type statement and a Hilbert-Samuel formula for a large class of singular plurisubharmonic metrics on a line bundle over a smooth projective complex variety. For this we use the theory of b-divisors and the so-called multiplier ideal volume function. We apply our results to the line bundle of Siegel-Jacobi forms over the universal abelian variety endowed with its canonical invariant metric. This generalizes the results of [J. I. Burgos Gil et al., Lond. Math. Soc. Lect. Note Ser. 427, 45--77 (2016; Zbl 1378.14027)] to higher degrees.Number theory, Algebra and Geometr

Correspondences in Arakelov geometry and applications to the case of Hecke operators on modular curves

In the context of arithmetic surfaces, Bost defined a generalized Arithmetic Chow Group (ACG) using the Sobolev space L^2_1. We study the behavior of these groups under pull-back and push-forward and we prove a projection formula. We use these results to define an action of the Hecke operators on the ACG of modular curves and to show that they are self-adjoint with respect to the arithmetic intersection product. The decomposition of the ACG in eigencomponents which follows allows us to define new numerical invariants, which are refined versions of the self-intersection of the dualizing sheaf. Using the Gross-Zagier formula and a calculation due independently to Bost and Kuehn we compute these invariants in terms of special values of L series. On the other hand, we obtain a proof of the fact that Hecke correspondences acting on the Jacobian of the modular curves are self-adjoint with respect to the N\'eron-Tate height pairing.Comment: 38 pages. Minor correction

Positivity of the height jump divisor

We study the degeneration of semipositive smooth hermitian line bundles on open complex manifolds, assuming that the metric extends well away from a codimension two analytic subset of the boundary. Using terminology introduced by R. Hain, we show that under these assumptions the so-called height jump divisors are always effective. This result is of particular interest in the context of biextension line bundles on Griffiths intermediate jacobian fibrations of polarized variations of Hodge structure of weight −1⁠, pulled back along normal function sections. In the case of the normal function on M_g associated to the Ceresa cycle, our result proves a conjecture of Hain. As an application of our result we obtain that the Moriwaki divisor on M_g  has non-negative degree on all complete curves in M_g not entirely contained in the locus of irreducible singular curves.Number theory, Algebra and Geometr

International Nosocomial Infection Control Consortium report, data summary of 50 countries for 2010-2015: Device-associated module

•We report INICC device-associated module data of 50 countries from 2010-2015.•We collected prospective data from 861,284 patients in 703 ICUs for 3,506,562 days.•DA-HAI rates and bacterial resistance were higher in the INICC ICUs than in CDC-NHSN's.•Device utilization ratio in the INICC ICUs was similar to CDC-NHSN's. Background: We report the results of International Nosocomial Infection Control Consortium (INICC) surveillance study from January 2010-December 2015 in 703 intensive care units (ICUs) in Latin America, Europe, Eastern Mediterranean, Southeast Asia, and Western Pacific. Methods: During the 6-year study period, using Centers for Disease Control and Prevention National Healthcare Safety Network (CDC-NHSN) definitions for device-associated health care-associated infection (DA-HAI), we collected prospective data from 861,284 patients hospitalized in INICC hospital ICUs for an aggregate of 3,506,562 days. Results: Although device use in INICC ICUs was similar to that reported from CDC-NHSN ICUs, DA-HAI rates were higher in the INICC ICUs: in the INICC medical-surgical ICUs, the pooled rate of central line-associated bloodstream infection, 4.1 per 1,000 central line-days, was nearly 5-fold higher than the 0.8 per 1,000 central line-days reported from comparable US ICUs, the overall rate of ventilator-associated pneumonia was also higher, 13.1 versus 0.9 per 1,000 ventilator-days, as was the rate of catheter-associated urinary tract infection, 5.07 versus 1.7 per 1,000 catheter-days. From blood cultures samples, frequencies of resistance of Pseudomonas isolates to amikacin (29.87% vs 10%) and to imipenem (44.3% vs 26.1%), and of Klebsiella pneumoniae isolates to ceftazidime (73.2% vs 28.8%) and to imipenem (43.27% vs 12.8%) were also higher in the INICC ICUs compared with CDC-NHSN ICUs. Conclusions: Although DA-HAIs in INICC ICU patients continue to be higher than the rates reported in CDC-NSHN ICUs representing the developed world, we have observed a significant trend toward the reduction of DA-HAI rates in INICC ICUs as shown in each international report. It is INICC's main goal to continue facilitating education, training, and basic and cost-effective tools and resources, such as standardized forms and an online platform, to tackle this problem effectively and systematically