Transcendental Brauer groups of products of CM elliptic curves

Let L be a number field and let E/L be an elliptic curve with complex multiplication by the ring of integers O_K of an imaginary quadratic field K. We use class field theory and results of Skorobogatov and Zarhin to compute the transcendental part of the Brauer group of the abelian surface ExE. The results for the odd order torsion also apply to the Brauer group of the K3 surface Kum(ExE). We describe explicitly the elliptic curves E/Q with complex multiplication by O_K such that the Brauer group of ExE contains a transcendental element of odd order. We show that such an element gives rise to a Brauer-Manin obstruction to weak approximation on Kum(ExE), while there is no obstruction coming from the algebraic part of the Brauer group.

Realising the cup product of local Tate duality

We present an explicit description, in terms of central simple algebras, of a cup product map which occurs in the statement of local Tate duality for Galois modules of prime cardinality p. Given cocycles f and g, we construct a central simple algebra of dimension p^2 whose class in the Brauer group gives the cup product f\cup g. This algebra is as small as possible.

Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory

2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20.

A randomised controlled trial of an enhanced interdisciplinary community based group program for people with Parkinson’s disease: study rationale and protocol

Parkinson’s disease (PD) is a progressive, chronic neurodegenerative disorder for which there is no known cure. Physical exercise programs may be used to assist with the physical management of PD. Several studies have demonstrated that community based physical therapy programs are effective in reducing physical aspects of disability among people with PD. While multidisciplinary therapy interventions may have the potential to reduce disability and improve the quality of life of people with PD, there is very limited clinical trial evidence to support or refute the use of a community based multidisciplinary or interdisciplinary programs for people with PD. A two group randomized trial is being undertaken within a community rehabilitation service in Brisbane, Australia. Community dwelling adults with a diagnosis of Idiopathic Parkinson’s disease are being recruited. Eligible participants are randomly allocated to a standard exercise rehabilitation group program or an intervention group which incorporates physical, cognitive and speech activities in a multi-tasking framework. Outcomes will be measured at 6-week intervals for a period of six months. Primary outcome measures are the Montreal Cognitive Assessment (MoCA) and the Timed Up and Go (TUG) cognitive test. Secondary outcomes include changes in health related quality of life, communication, social participation, mobility, strength and balance, and carer burden measures. This study will determine the immediate and long-term effectiveness of a unique multifocal, interdisciplinary, dual-tasking approach to the management of PD as compared to an exercise only program. We anticipate that the results of this study will have implications for the development of cost effective evidence based best practice for the treatment of people with PD living in the community.