Counting Rational Points on K3 Surfaces

For any algebraic variety $V$ defined over a number field $k$, and ample height function $H$ on $V$, one can define the counting function N_V(B) = #{P\in V(k) \mid H(P)\leq B}. In this paper, we calculate the counting function for Kummer surfaces $V$ whose associated abelian surface is the product of elliptic curves. In particular, we effectively construct a finite union $C = \cup C_i$ of curves $C_i$ on $V$ such that $N_{V-C}(B)\ll N_C(B)$; that is, $C$ is an accumulating subset of $V$. In the terminology of Batyrev and Manin, this amounts to proving that $C$ is the first layer of the arithmetic stratification of $V$.Comment: LaTeX, 9 pages, no figures. Typo corrected, acknowledgements added, a few minor clarification

Should we tolerate climate denial?

At 18.27 on 12 December 2015, Laurent Fabius brought down his gavel to mark the adoption of the Paris Agreement by nearly 200 countries. Even the most optimistic commentators agree that the scale and speed of the action needed to realize the ambitions of the Agreement are daunting. The history of action on climate change gives us no grounds for optimism. But perhaps, we still have grounds for hope (McKinnon 2014). Many things could snuff out this fragile hope. In this article, I shall address conduct that explicitly aims to do so: climate change denial (from here on in, “climate denial”). By “climate denial,” I mean the deliberate and deceptive misrepresentation of the scientific realities of climate change, such as the fact that climate change is happening, its anthropogenic causes, and its damaging impacts (Dunlap 2013). What I do not mean by “climate denial” are minority or outlier positions on aspects of climate science that lie within the range of normal and healthy disciplinary disagreement. There is an established international network of well-funded organizations devoted to organized climate denial, and their activity is on the increase (Boussalis and Coan 2016). The epicenter of this activity is in the United States, where climate denial has had a significant impact on public opinion (Leiserowitz et al. 2014), and has impeded legislation to tackle climate change (Farrell 2016; Oreskes and Conway 2012). My question is: should we tolerate climate denial? The “we” in this question refers to broadly liberal people and legislators in democratic societies, for whom principles of toleration and the virtue of tolerance are of fundamental importance in social and political life. Toleration is a matter of principled self-restraint with respect to conduct that would alter, suppress, or prevent the characteristics or conduct of people opposed by the tolerator (McKinnon 2006; McKinnon and Castiglione 2003). The tolerant agent refrains from interfering with those she dislikes or of whom she disapproves even when she believes that her dislike or disapproval is well-grounded. The agents of toleration can be individual people—when toleration is likely to manifest as a virtue, or as a civic disposition—or institutions, when fundamental political principles, the constitution, and laws and their implementation, are framed to respect the limits of toleration (McKinnon 2013). Toleration is difficult to justify and hard to practice at both the personal and institutional level, particularly for liberals (Scanlon 2003a). Liberalism is committed to freedom of association, conscience, worship, movement, and expression as a matter of fundamental principle (Rawls 1971). This delivers a distinctive liberal, permissive vision of the limits of toleration with respect to acts of expression. Given that climate denial is achieved through acts of expression, there is a heavy burden of proof attached to any liberal proposal to be intolerant of climate denial.1 My aim in this short article is to identify the proper site for this debate. What are the questions to be answered in deciding whether climate denial lies beyond the limits of liberal toleration? Although I do not answer these questions, by correctly identifying them I hope to show that the burden of proof is perhaps not as heavy as we initially might have thought

Current Research: Toward a Collaborative Development of a Truly Comprehensive Multi-State Material Culture Database

Throughout the past several years, I have been compiling, with the help of several Caddo researchers, a comprehensive multi-state database primarily composed of whole Caddo vessels from published excavations, private collections, and archaeological reports. At present, the database contains over 13,000 vessel entries from over 500 sites ranging from a single vessel recorded at a site to hundreds. Over the years, the database has evolved to contain, where applicable, attribute fields on type, variety, motif designs (largely using the Glossary of Motifs published in the Spiro shell engravings, collegiate assignment, form, temper, decorative method (incised, brushed, etc.), context (burial #, site #, intra site location), pigment, archaeological phase, collector, repository, associated photographs, and reference citations. The database is managed using Microsoft Access where data are imported into ESRI ArcGIS and spatial analyses can be conducted. This is a continual, and perhaps never-ending, work in progress where attribute fields are added, types are vetted, and new sites are included. In some cases, “Caddo-like” vessels from sites outside the Caddo Archaeological Area, or Caddo Homeland, are included in order to evaluate social interaction and exchange of ideas. Through this process, some initial insights into landscape scale social interactions and interregional relationships using this growing comprehensive database have been explored

A Report on a Long Term Research Program on the Bowman site in Arkansas

The Bowman (3LR46) and Bowman/Wallace (3LR50) sites represent a Caddo multi-mound center on the Red River in Little River County, Arkansas. Southeastern researchers may recognize the site name from an engraved shell cup and several additional “SECC” objects found in Mound 2. Hoffman provides a brief summary of digging at the sites and offers a proposed site organization of eight mounds (both burial and “temple mounds”) surrounding a possible plaza area and at least three offmound cemeteries. Material collected from Mounds 1 and 2 and two off-mound cemeteries suggest Haley phase (ca. A.D. 1200-1400) occupations. Additionally, data from Mound 1 have the potential to “reveal a solid sequence of [Caddo] burial and mortuary artifact styles” beginning with the earliest Caddo occupations in the Red River region

Metaphors in and for the Sociology of Religion : Towards a Theory after Nietzsche

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