A note on the ramification of torsion points lying on curves of genus at least two

Let $C$ be a curve of genus $g\geqslant 2$ defined over the fraction field $K$ of a complete discrete valuation ring $R$ with algebraically closed residue field. Suppose that \char(K)=0 and that the characteristic of the residue field is not 2. Suppose that the Jacobian \Jac(C) has semi-stable reduction over $R$. Embed $C$ in \Jac(C) using a $K$-rational point. We show that the coordinates of the torsion points lying on $C$ lie in the unique moderately ramified quadratic extension of the field generated over $K$ by the coordinates of the $p$-torsion points on \Jac(C)

The distribution of class groups of function fields

Using equidistribution results of Katz and a computation in finite symplectic groups, we give an explicit asymptotic formula for the proportion of curves C over a finite field for which the l-torsion of Jac(C) is isomorphic to a given abelian l-group. In doing so, we prove a conjecture of Friedman and WashingtonComment: To appear, JPA

Economic Freedom and Economic Growth: A Short-run Causal Investigation

The freedom and growth literature has consistently shown that nations which have fewer restrictions on private agents and transactions tend to higher levels of economic growth. It is less clear, however, whether freedom causes growth, growth causes freedom, or the two are jointly determined. To assess these possibilities, Granger-causality tests are performed on annual freedom indicators developed by the Heritage Foundation and national growth rates. The underlying component indexes, which include Trade Policy, Taxation, Government Intervention, Monetary Policy, Capital Flows and Foreign Investment, Banking, Wage and Price Controls, Property Rights, Regulation, and Black Markets, are also tested in addition to the summary freedom rating. The tests suggest the average level of freedom in a nation, as well as many of the specific underlying components of freedom, precedes growth. However, growth may precede one of the component indexes (Government Intervention), and no relationship is found to exist between growth and two of the indexes (Trade Policy and Taxation).economic freedom; economic growth; Granger-causality

Has assistance from USAID been successful in promoting and sustaining democracy? Evidence from the transition economies of Eastern Europe and Eurasia

Foreign aid, especially official development assistance (ODA), has received increasing criticism in past decades. In particular, it has been put into question if and to what extent aid can help foster the aims for which it has been paid. In most cases, it seems that there is no discernable effect or even a negative effect of ODA on economic development. One reason for aid ineffectiveness may be seen in a lack of good governance on the side of the recipients. It has been argued that aid should concentrate more on creating better institutions. In the past 20 years, democracy promotion has become a pillar of USAID's mission and the funding for democracy and governance has steadily increased. The transition economies in particular have received special attention upon the fall of the Soviet Union. We assess the success of this aid by testing whether US aid is enhancing democracy in 26 transition countries. Using Freedom House Nations in Transit data, we find that in simple linear panel regressions aid has generally not been a significant factor in a country's overall democracy score. However, aid has significantly contributed to certain components of the democracy score, namely civil society, electoral process, judicial framework, and media independence. In addition, the impact of aid is found to depend on the number of years of past central planning. Countries having a history of less than 50 years of central planning had a significantly negative association to aid, whereas countries with more than 65 years of central planning benefited from greater aid.ODA, transition economies, democracy

Corruption and the Institutional Environment for Growth

Several cross-country studies have found that corruption is detrimental to economic growth, but the findings are not universally robust. We utilize the economic freedom index to examine if corruption can facilitate growth by allowing entrepreneurs to avoid inefficient policies and regulations when economic freedom is limited. Using regression analysis, we find that corruption is growth enhancing when economic freedom is most limited but the beneficial impact of corruption decreases as economic freedom increases. Not all areas of economic freedom affect the corruption-growth relationship equally. In particular, we find that when we analyze individual areas of economic freedom the beneficial effect of corruption disappears most quickly when the size of government and the extent of regulation decrease.Corruption; Economic Freedom; Growth

Normal Functions and the Geometry of Moduli Spaces of Curves

In this paper normal functions (in the sense of Griffiths) are used to solve and refine geometric questions about moduli spaces of curves. The first application is to a problem posed by Eliashberg: compute the class in the cohomology of M_{g,n}^c of the pullback of the zero section of the universal jacobian along the section that takes [C;x_1,...,x_n] to Sum d_j x_j in Jac (C), where d_1 + ... + d_n = 0. The second application is to slope inequalities of the type discovered by Moriwaki. There is also a discussion of height jumping and its relevance to slope inequalilties.Comment: Updated to published version. Also added publication informatio

SIZE OF THE MILITARY SECTOR AND ECONOMIC GROWTH: A PANEL DATA ANALYSIS OF AFRICA AND LATIN AMERICA

We estimate the influence of defense spending and military labor use on economic growth in African and Latin American countries. Our model integrates disparate implications from the defense economics literature into a Barro-style model of economic growth that controls for political and economic institutional variation across countries. Our panel data analysis of 44 countries in Africa and Latin America from 1975 to 1989 also controls for cross-country variation in lost human capital and public sector production inefficiencies. We find empirical evidence that the defense burden on economic growth is non-linear, with low levels of military spending increasing economic growth but higher levels of military spending decreasing growth. We also find evidence that the influence of military labor use on growth is non-linear, and exhibits a greater drag on economic growth in those countries with relatively higher levels of adult male education attainment.defense burden; economic growth

Doubly isogenous genus-2 curves with D₄-action

We study the extent to which curves over finite fields are characterized by their zeta functions and the zeta functions of certain of their covers. Suppose C and C are curves over a finite field K, with K-rational base points P and P , and let D and D be the pullbacks (via the Abel–Jacobi map) of the multiplication-by-2 maps on their Jacobians. We say that (C, P) and (C , P ) are doubly isogenous if Jac(C) and Jac(C ) are isogenous over K and Jac(D) and Jac(D ) are isogenous over K. For curves of genus 2 whose automorphism groups contain the dihedral group of order eight, we show that the number of pairs of doubly isogenous curves is larger than na¨ıve heuristics predict, and we provide an explanation for this phenomenon