Gerbes and Brauer groups over stacks

The aim of this paper is to develop the theory of Brauer groups for stacks, which are not necessarily algebraic, using gerbes as foundamental tools. As an application, we focus our attention on Brauer theory for mixed motives: in particular, over a normal base scheme, we prove the generalized Theorem of the Cube for 1-motives and that a torsion class of the H^2_et(M,G_m) of a 1-motive M, whose pull-back via the unit section is zero, comes from an Azumaya algebra. Over an algebraically closed field, all classes of H^2_et(M,G_m) come from Azumaya algebras.Comment: We add a section about 2-descent theory for stack

The polarimetric multi-frequency radio sources properties

The polarization properties of extragalactic radio sources at frequencies higher than 20 GHz are still poorly constrained. However, their characterization would provide invaluable information about the physics of the emission processes and is crucial to estimate their contamination as foregrounds of the polarized cosmic microwave background (CMB) angular power spectrum on scales < 30 arcmin. In this contribution, after summarizing the state-of-the-art of polarimetric observations in the millimetric wavelength bands, we present our observations of a complete sample of 53 sources with S > 200 mJy (at 20 GHz) carried out with the Australia Telescope Compact Array between 5.5 and 38 GHz. The analysis clearly shows that polarization properties cannot be simply inferred from total intensity ones, as the spectral behaviors of the two signals are typically different

A note on divisorial correspondences of extensions of abelian schemes by tori

Let S be a locally noetherian scheme and consider two extensions G_1 and G_2 of abelian S-schemes by S-tori. In this note we prove that the fppf-sheaf Corr _S(G_1,G_2) of divisorial correspondences between G_1 and G_2 is representable. Moreover, using divisorial correspondences, we show that line bundles on an extension G of an abelian scheme by a torus define group homomorphisms between G and Pic_{ G/S}.Comment: new versio

Conservation and use of genetic resources of underutilized crops in the Americas - A continental analysis

Latin America is home to dramatically diverse agroecological regions which harbor a high concentration of underutilized plant species, whose genetic resources hold the potential to address challenges such as sustainable agricultural development, food security and sovereignty, and climate change. This paper examines the status of an expert-informed list of underutilized crops in Latin America and analyses how the most common features of underuse apply to these. The analysis pays special attention to if and how existing international policy and legal frameworks on biodiversity and plant genetic resources effectively support or not the conservation and sustainable use of underutilized crops. Results show that not all minor crops are affected by the same degree of neglect, and that the aspects under which any crop is underutilized vary greatly, calling for specific analyses and interventions. We also show that current international policy and legal instruments have so far provided limited stimulus and funding for the conservation and sustainable use of the genetic resources of these crops. Finally, the paper proposes an analytical framework for identifying and evaluating a crop’s underutilization, in order to define the most appropriate type and levels of intervention (international, national, local) for improving its statu

The Nori-Hilbert scheme is not smooth for 2-Calabi Yau algebras

Let $k$ be an algebraically closed field of characteristic zero and let $A$ be a finitely generated $k-$algebra. The Nori - Hilbert scheme of $A$, parameterizes left ideals of codimension $n$ in $A,$ and it is well known to be smooth when $A$ is formally smooth. In this paper we will study the Nori - Hilbert scheme for $2-$Calabi Yau algebras. The main examples of these are surface group algebras and preprojective algebras. For the former we show that the Nori-Hilbert scheme is smooth for $n=1$ only, while for the latter we show that the smooth components that contain simple representations are precisely those that only contain simple representation. Under certain conditions we can generalize this last statement to arbitrary $2-$Calabi Yau algebras.Comment: 30 pages, research paper. Accepted for publication in Journal of Noncommutative Geometr