The Brauer-Manin obstruction on Kummer varieties and ranks of twists of abelian varieties

Let r > 0 be an integer. We present a sufficient condition for an abelian variety A over a number field k to have infinitely many quadratic twists of rank at least r, in terms of density properties of rational points on the Kummer variety Km(A^r) of the r-fold product of A with itself. One consequence of our results is the following. Fix an abelian variety A over k, and suppose that for some r > 0 the Brauer-Manin obstruction to weak approximation on the Kummer variety Km(A^r) is the only one. Then A has a quadratic twist of rank at least r. Hence if the Brauer-Manin obstruction is the only one to weak approximation on all Kummer varieties, then ranks of twists of any positive-dimensional abelian variety are unbounded. This relates two significant open questions.Comment: 12 pages; final versio

Who matters? Public history and the invention of the Canadian past

There is no longer any real dispute that the past, as distinct from traditions, is an invention based on a careful selection of apparently empirical evidence. Historians now accept that there is no "ultimate" truth; there are many perspectives or narratives, all valid and all exploring new realities and new truths. The current multi-streamed discourse in history, however, is fraught with impossible challenges for public historians. Some narratives focus on a heritage of achievement and triumph. Others will focus on exploitation and marginalization, which will in turn be denied by the narratives of the exploiters. Not all narratives can be accommodated equally without creating problems of imbalance or a diet of pablum. Such is the conundrum of the Canadian historian who would like to achieve that pleasant Canadian nirvana ? consensus

Metis Studies : The Development of a Field and New Directions

Until recently, sources for Mets studies have been few both for classroom use as well as academic reflection. Lately, there has been a virtual explosion of interest, although largely among non-Mets historians. Now this to has begun to change. A new dynamic is also forcing Metis historiography out of the bog Red River in which some argue it has been mired for too long. The writings of the previous decades have already been examined from a historiographical perspective in several excellent articles. Rather than updating these useful exercises, an alternative is to examine the new literature from a topical perspective, posing questions and suggesting new avenues of investigation. The current literature is the reflection of scholarly concerns of the last two decades and fit into six basic themes or areas: the origins of the Mets people, the historic Mets of the fur trade period of the eighteenth and early nineteenth century, the Mets Diaspora of the mid to late nineteenth century, the revival of Mets consciousness in the twentieth century, Mets land claims, and Mets women's history. A case could be made that the beginning point in each of these areas are the great icons of Mets historiography: W.L. Morton, G.F.G. Stanley, and Marcel Giraud. However, their studies have been well assessed and often reinforce stereotypes, so it is best to look to more recent literature

Calibrated imputation of numerical data under linear edit restrictions

A common problem faced by statistical offices is that data may be missing from collected data sets. The typical way to overcome this problem is to impute the missing data. The problem of imputing missing data is complicated by the fact that statistical data often have to satisfy certain edit rules and that values of variables sometimes have to sum up to known totals. Standard imputation methods for numerical data as described in the literature generally do not take such edit rules and totals into account. In the paper we describe algorithms for imputation of missing numerical data that do take edit restrictions into account and that ensure that sums are calibrated to known totals. The methods sequentially impute the missing data, i.e. the variables with missing values are imputed one by one. To assess the performance of the imputation methods a simulation study is carried out as well as an evaluation study based on a real dataset

Canadian memory institutions and the digital revolution : the last five years

Three American companies carry 80 per cent of Internet traffic. America Online has a large financial interest in two of these companies. Today there are about 1.5 million connections to the Internet; by 2010 there will be 1.5 billion. From 1993 to 1997 graphic content moved from zero per cent to 14 per cent; by 2010 it will dominate. The average capital cost to access the Internet is about $3,000, with an annual operating cost of$400 - enough in most of the world to support a family of four for a year. Over 90 per cent of all communication on the Internet is in English, and most activity on the Internet is commercial. In 1980 there were 411 digital databases; in 1997 there are over 10,000. Over 57 per cent of University of Calgary undergraduates prefer to access information in digital form. Only two to three universities in Canada can afford all the available databases and full text materials. A 2000 University of Calgary study for the Social Science and Humanities Federation indicates that there are only two hundred Canadian sites that meet basic scholarly standards. Six vendors control most of the key academic databases. Fifty-seven per cent of Canadian scholars who identified a reason for not using electronic resources indicated that they were not credible (Archer 2000, Table 6).' What sense can be made of these apparently random numbers and events? Castells (1997) has offered a profound analysis. He argues that we are in the midst of an "information technology revolution" that is "pervasive" and which is influencing social and economic interactions. He would argue further that the adaptations of the new technologies depend very much on national identities and cultures. It should be noted, however, that in his approximately fifteen hundred pages he does not mention libraries, archives or museums even once. If one acknowledges these memory institutions as players in the new information age, however, several conclusions become apparent. First, the "cultural democracy" of the Internet is athe moment an illusion. Content creation and access still rests with a few Western, English-speaking information aggregators who have their roots in commerce rather than in intellectual pursuits or culture. Second, there is an even more concentrated control over the best Web content than there ever was over print. This is in part because the technical capacities of the digital environment allow for the perfect commodification and control of information. Third, the early stages of content and technology development were undertaken by American government agencies, for example the National Science Foundation. Leadership has now been handed of to the private sector. Sprint, Ameritech, and Microsoft now dominate technology, and Thomson and Elsevier high-end content. And the library world's OCLC (Online Computer Library Center), the American-based information collaborative, is beginning to dominate the English-speaking post-secondary world

Alberta : A Community Development Heritage Alternative

Since 1980, twelve new heritage attractions have been constructed by the Province of Alberta with three new facilities opening since 1990 despite a major recession. All but the Royal Tyrrell Museum and its Field Station were built by the Historic Sites Service of the Department of Culture, formerly of the Department of Culture and Multiculturalism, and now a branch of the Department of Community Development. On the average, these facilities have cost some $10 million each. Along with five sites built before 1980, they attract some one million visitors annually, and contribute over$25 million to the local and $5 million to the provincial economies

Some comments on the social origins of the Riel Protest of 1869

The English-speaking folk of Red River looked with excitement and hope on the debates that surrounded the confederation of the eastern provinces. The Protestant Canadians, arriving in vocal and visible numbers in the 1860s to farm along the Assiniboine and to trade in the small village of Winnipeg, provided ample evidence of the vigour that the new connection would bring. All were anxious that union be effected quickly and quietly. Even the Protestant English speaking mixed-bloods looked to Canada to pull Red River out of its morass of pettiness and squalor. When it became clear that Canada had secured the chartered land of the Hudson's Bay Company, most were ready, indeed anxious, to welcome the Canadian Governor, no matter how obnoxious he might be. (Metis