Cyclic Algebras over pp-adic curves

In this paper we study division algebras over the function fields of curves over \Q_p. The first and main tool is to view these fields as function fields over nonsingular $S$ which are projective of relative dimension 1 over the $p$ adic ring $\Z_p$. A previous paper showed such division algebras had index bounded by $n^2$ assuming the exponent was $n$ and $n$ was prime to $p$. In this paper we consider algebras of degree (and hence exponent) $q \not= p$ and show these algebras are cyclic. We also find a geometric criterion for a Brauer class to have index $q$

Invariant Fields of Symplectic and Orthogonal Groups

The projective orthogonal and symplectic groups $PO_n(F)$ and $PSp_n(F)$ have a natural action on the $F$ vector space $V' = M_n(F) \oplus ... \oplus M_n(F)$. Here we assume $F$ is an infinite field of characteristic not 2. If we assume there is more than one summand in $V'$, then the invariant fields $F(V')^{PO_n}$ and $F(V')^{PSp_n}$ are natural objects. They are, for example, the centers of generic algebras with the appropriate kind of involution. This paper considers the rationality properties of these fields, in the case $1,2$ or 4 are the highest powers of 2 that divide $n$. We derive rationality when $n$ is odd, or when 2 is the highest power, and stable rationality when 4 is the highest power. In a companion paper [ST] joint with Tignol, we prove retract rationality when 8 is the highest power of 2 dividing $n$. Back in this paper, along the way, we consider two generic ways of forcing a Brauer class to be in the image of restriction.Comment: 25 page

Urban School Decentralization and the Growth of "Portfolio Districts"

In the latter half of the past decade, school districts in several large cities, including New York, Chicago, Washington, D.C., and post-Katrina New Orleans, have implemented an urban school decentralization model generally known as "portfolio districts." Others, including those in Denver and Cleveland, are following suit in what appears to be a growing trend. The portfolio strategy has become increasingly prominent in educational policy circles, think tank and philanthropy literature, and education news reporting. As CEO of the Chicago Public Schools, Arne Duncan embraced the portfolio district model. His appointment as U.S. Secretary of Education suggests the Obama administration also supports the approach. The premise of the portfolio strategy is that if superintendents build portfolios of schools that encompass a variety of educational approaches offered by different vendors, then over time school districts will weed out under-performing approaches and vendors; as a result, more children will have more opportunities for academic success. This brief examines the available evidence for the viability of this premise and the proposals that flow from it.The portfolio district approach merges four strategies: 1) decentralization; 2) charter school expansion; 3) reconstituting/closing "failing" schools; and 4) test-based accountability. Additionally, portfolio district restructuring often involves firing an underperforming school's staff in its entirety, whether or not the school is reconstituted as a charter school. In this model, the portfolio district is conceptualized as a circuit of "continuous improvement." Schools are assessed based on test scores; if their scores are low, they are subject to being closed and reopened as charters. The replacement charters are subsequently subject to test-based assessment and, if scores remain disappointing, to possible closure and replacement by still other contractors. The portfolio district concept implements what has been since the 1990's discussed in educational policy literature as market-based "creative destruction" or "churn."1 This perspective considers public schools to be comparable to private enterprise, with competition a key element to success. Just as businesses that cannot turn sufficient profit, schools that cannot produce test scores higher than competitors' must be "allowed" to "go out of business." The appeal of the portfolio district strategy is that it appears to offer an approach sufficiently radical to address longstanding and intractable problems in public schools.Although the strategy is being advocated by some policy centers, implemented by some large urban districts, and promoted by the education reforms proposed as part of the Obama administrations Race to the Top initiative, no peer-reviewed studies of portfolio districts exist, meaning that no reliable empirical evidence about portfolio effects is available that supports either the implementation or rejection of the portfolio district reform model. Nor is such evidence likely to be forthcoming. Even advocates acknowledge the enormous difficulty of designing credible empirical studies to determine how the portfolio approach affects student achievement and other outcomes. There are anecdotal reports of achievement gains in one portfolio district, New Orleans. The New Orleans results, however, have been subjected to serious challenge. Extrapolation of research on the constituent elements of the model is not helpful because of the complex interactions of these elements within the portfolio model. Moreover, even when the constituent elements are considered as a way to predict the likely success of the model, no evidence is found to suggest that it will produce gains in either achievement or fiscal efficiency. Finally, the policy writing of supporters of the portfolio model suggests that the approach is expensive to implement and may have negative effects on student achievement.In light of these considerations, it is recommended that policymakers and administrators use caution in considering the portfolio district approach. It is also highly recommended that before adopting such a strategy, decision makers ask the following questions.What credible evidence do we have, or can we obtain, that suggests the portfolio model offers advantages compared to other reform models? What would those advantages be, when might they be expected to materialize, and howmight they be documented?If constituent elements of the model (such as charter schools and test-based accountability) have not produced advantages outside of portfolio systems, whatis the rationale for expecting improved outcomes as part of a portfolio system?What funding will be needed for startup, and where will it come from?What funding will be necessary for maintenance of the model? Where will continuation funds come from if startup funds expire and are not renewed?How will the cost/benefit ratio of the model be determined?What potential political and social conflicts seem possible? How will concerns of dissenting constituents be addressed

Generic algebras with involution of degree 8m

The centers of the generic central simple algebras with involution are interesting objects in the theory of central simple algebras. These fields also arise as invariant fields for linear actions of projective orthogonal or symplectic groups. In this paper, we prove that when the characteristic is not 2, these fields are retract rational, in the case the degree is $8m$ and $m$ is odd. We achieve this by proving the equivalent lifting property for the class of central simple algebras of degree $8m$ with involution. A companion paper ([S3]) deals with the case of $m$, $2m$ and $4m$ where stronger rationality results are proven.Comment: 7 page

A promessa e as realidades de Pay for Success/Social Impact Bonds

This article considers proponents’ arguments for Pay for Success also known as Social Impact Bonds. Pay for Success allows banks to finance public services with potential profits tied to metrics. Pay for Success has received federal support through the Every Student Succeeds Act of 2016 and is predicted by 2020 to expand in the US to a trillion dollars. As school districts, cities, and states face debt and budget crises, Pay for Success has been advocated by philanthropists, corporate consulting firms, politicians, and investment banks on the grounds of improving accountability, cost savings, risk transfer, and market discipline. With its trailblazing history in neoliberal education, Chicago did an early experiment in Pay for Success. This article provides a conceptual analysis of the key underlying assumptions and ideologies of Pay for Success. It examines the claims of proponents and critics and sheds light on the financial and ideological motivations animating Pay for Success. The article contends that Pay for Success primarily financially benefits banks without providing the benefits that proponents promise. It concludes by considering Pay for Success in relation to broader structural economic considerations and the recent uses of public schooling to produce short-term profit for capitalists. En este artículo se consideran los argumentos de los proponentes de Pay for Success, también conocidos como Social Impact Bonds. Pay for Success permite a los bancos financiar servicios públicos con beneficios potenciales vinculados a métricas. Pagar por el Éxito ha recibido apoyo federal a través de la Ley de Todos los Sucesos Sucesivos de 2016 y está previsto para 2020 para expandirse en los EE.UU. a un billón de dólares. A medida que los distritos escolares, las ciudades y los estados se enfrentan a crisis de deuda y presupuesto, Pay for Success ha sido defendido por filántropos, empresas de consultoría corporativa, políticos y bancos de inversión con el fin de mejorar la rendición de cuentas, ahorro de costos, transferencia de riesgos y disciplina de mercado. Con su historia pionera en la educación neoliberal, Chicago hizo un experimento temprano en Pay for Success. Este artículo provee un análisis conceptual de las suposiciones e ideologías fundamentales de Pay for Success. Examina las afirmaciones de los defensores y críticos y arroja luz sobre las motivaciones financieras e ideológicas que animan a Pay for Success. El artículo sostiene que pagar por el éxito beneficia principalmente a los bancos sin proporcionar los beneficios que los proponentes prometen. Concluye considerando el Pay For Success en relación con consideraciones económicas estructurales más amplias y los usos recientes de la educación pública para producir ganancias a corto plazo para los capitalistas.Este artigo considera os argumentos dos proponentes para Pay for Success, também conhecidos como “Social Impact Bonds”. Pay for Success permite aos bancos financiar serviços públicos com lucros potenciais ligados a métricas. Pagar pelo sucesso recebeu apoio federal através da Lei de Sucesso de Todos os Estudantes de 2016 e está prevista para 2020 para expandir nos EUA para um trilhão de dólares. À medida que os distritos escolares, as cidades e os estados enfrentam crises de dívida e orçamento, Pay for Success foi defendido por filantropos, empresas de consultoria corporativa, políticos e bancos de investimento com base em melhorar a prestação de contas, redução de custos, transferência de riscos e disciplina de mercado. Com sua história pioneira na educação neoliberal, Chicago fez uma experiência inicial em Pay for Success. Este artigo fornece uma análise conceitual dos principais pressupostos subjacentes e ideologias do Pay for Success. Ele examina as reivindicações de defensores e críticos e ilumina as motivações financeiras e ideológicas que animam Pay for Success. O artigo afirma que o Pay for Success beneficia principalmente os bancos sem beneficiar dos benefícios que os proponentes prometem. Conclui considerando Pay for Success em relação a considerações econômicas estruturais mais amplas e os recentes usos da educação pública para produzir lucro a curto prazo para os capitalistas