Representation fields for commutative orders

A representation field for a non-maximal order \Ha in a central simple algebra is a subfield of the spinor class field of maximal orders which determines the set of spinor genera of maximal orders containing a copy of \Ha. Not every non-maximal order has a representation field. In this work we prove that every commutative order has a representation field and give a formula for it. The main result is proved for central simple algebras over arbitrary global fields.Comment: Annales de l'institut Fourier, vol 61, 201

Roots of unity in definite quaternion orders

A commutative order in a quaternion algebra is called selective if it is embeds into some, but not all, the maximal orders in the algebra. It is known that a given quadratic order over a number field can be selective in at most one indefinite quaternion algebra. Here we prove that the order generated by a cubic root of unity is selective for any definite quaternion algebra over the rationals with a type number 3 or larger. The proof extends to a few other closely related orders

Learning through the waste: olfactory cues from the colony refuse influence plant preferences in foraging leaf-cutting ants

Leaf-cutting ants learn to avoid plants initially harvested if they proved to be harmful for their symbiotic fungus once incorporated into the nest. By this time, waste particles removed from the garden likely contain cues originating from both the unsuitable plant and the damaged fungus. We investigated whether leaf-cutting ant foragers learn to avoid unsuitable plants solely through the colony waste. We fed subcolonies of Acromymex ambiguus privet leaves treated with a fungicide undetectable for the ants, collected later the produced waste, and placed it into the fungus chamber of naïve subcolonies. In individual choice tests, naïve foragers preferred privet leaves before, but avoided them after waste was given into the fungus chamber. Evidence on the influence of olfactory cues from the waste on decision making by foragers was obtained by scenting and transferring waste particles from subcolonies that had been fed either fungicide-treated or untreated leaves. In choice experiments, foragers from subcolonies given scented waste originating from fungicide-treated leaves collected less sugared paper disks smelling to it, as compared to foragers from subcolonies given scented waste from untreated leaves. Results indicate that foragers learn to avoid plants unsuitable for the fungus by associating plant odours and cues from the damaged fungus that are contingent in waste particles. It is argued that waste particles may contribute to spread information about noxious plants for the fungus within the colony.Fil: Arenas, Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Fisiología, Biología Molecular y Neurociencias. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Fisiología, Biología Molecular y Neurociencias; Argentina. Universität Würzburg; AlemaniaFil: Roces, Flavio. Universität Würzburg; Alemani