Hermitian structures on the derived category of coherent sheaves

The main objective of the present paper is to set up the theoretical basis and the language needed to deal with the problem of direct images of hermitian vector bundles for projective non-necessarily smooth morphisms. To this end, we first define hermitian structures on the objects of the bounded derived category of coherent sheaves on a smooth complex variety. Secondly we extend the theory of Bott-Chern classes to these hermitian structures. Finally we introduce the category \oSm_{\ast/\CC} whose morphisms are projective morphisms with a hermitian structure on the relative tangent complex

An arithmetic Hilbert-Samuel theorem for singular hermitian line bundles and cusp forms

We prove an arithmetic Hilbert-Samuel type theorem for semi-positive singular hermitian line bundles of finite height. In particular, the theorem applies to the log-singular metrics of Burgos-Kramer-K\"uhn. Our theorem is thus suitable for application to some non-compact Shimura varieties with their bundles of cusp forms. As an application, we treat the case of Hilbert modular surfaces, establishing an arithmetic analogue of the classical result expressing the dimensions of spaces of cusp forms in terms of special values of Dedekind zeta functions

Review of Body Mass Index Reduction Interventions among Mexican Origin Latinos and Latinas

Objectives: A literature review was conducted to identify factors associated with successful Body Mass Index (BMI) reduction interventions for Mexican origin US Hispanic/Latino populations. Data Source: An academic database search was conducted of peer-reviewed literature primarily in public health, medical anthropology, medical sociology, and biomedical databases. The key search words used were “Latino or Hispanic or Mexican”, in combination with “intervention”, “obesity”, “body mass index”, “weight reduction”, “best practices” and “lessons learned”. Inclusion Criteria: The inclusion criteria included an intervention protocol, with BMI measures, and a majority of participants identified as Mexican origin Hispanics. Search results yielded a total of 118 articles with 19 studies meeting the inclusion criteria. Results: The review found that education and the use of culturally tailored/sensitive materials are important factors in BMI reduction. In addition, the study found that family centered and community based approaches are some of the most successful evidence based practices found in the Latino health literature. Conclusions: Obesity and its sequelae disproportionately impact both US and non-US Latino/ Hispanic communities and have life-long and intergenerational consequences. The findings from this review may serve as a guide to the development of more successful interventions and best practices to address the needs of Mexican origin Latino populations