Postmodernism, or, the Cultural Logic of Late Capitalism

This is a review of Collected Works of John Tate. Parts I, II, edited by Barry Mazur and Jean-Pierre Serre. American Mathematical Society, Providence, Rhode Island, 2016. For several decades it has been clear to the friends and colleagues of John Tate that a “Collected Works” was merited. The award of the Abel Prize to Tate in 2010 added impetus, and finally, in Tate’s ninety-second year we have these two magnificent volumes, edited by Barry Mazur and Jean-Pierre Serre. Beyond Tate’s published articles, they include five unpublished articles and a selection of his letters, most accompanied by Tate’s comments, and a collection of photographs of Tate. For an overview of Tate’s work, the editors refer the reader to [4]. Before discussing the volumes, I describe some of Tate’s work. 1. Hecke L-series and Tate’s thesis Like many budding number theorists, Tate’s favorite theorem when young was Gauss’s law of quadratic reciprocity. When he arrived at Princeton as a graduate student in 1946, he was fortunate to find there the person, Emil Artin, who had discovered the most general reciprocity law, so solving Hilbert’s ninth problem. By 1920, the German school of algebraic number theorists (Hilbert, Weber, . . .) together with its brilliant student Takagi had succeeded in classifying the abelian extensions of a number field K: to each group I of ideal classes in K, there is attached an extension L of K (the class field of I); the group I determines the arithmetic of the extension L/K, and the Galois group of L/K is isomorphic to I. Artin’s contribution was to prove (in 1927) that there is a natural isomorphism from I to the Galois group of L/K. When the base field contains an appropriate root of 1, Artin’s isomorphism gives a reciprocity law, and all possible reciprocity laws arise this way. In the 1930s, Chevalley reworked abelian class field theory. In particular, he replaced “ideals” with his “idèles” which greatly clarified the relation between the local and global aspects of the theory. For his thesis, Artin suggested that Tate do the same for Hecke L-series. When Hecke proved that the abelian L-functions of number fields (generalizations of Dirichlet’s L-functions) have an analytic continuation throughout the plane with a functional equation of the expected type, he saw that his methods applied even to a new kind of L-function, now named after him. Once Tate had developed his harmonic analysis of local fields and of the idèle group, he was able prove analytic continuation and functional equations for all the relevant L-series without Hecke’s complicated theta-formulas. Received by the editors September 5, 2016. 2010 Mathematics Subject Classification. Primary 01A75, 11-06, 14-06. c ©2017 American Mathematical Society

The collected works

Scholars of culture, humanities and social sciences have increasingly come to an appreciation of the importance of the legal domain in social life, while critically engaged socio-legal scholars around the world have taken up the task of understanding "Law's Empire" in all of its cultural, political, and economic dimensions. The questions arising from these intersections, and addressing imperialisms past and present forms the subject matter of a special symposium issue of Social Identities under the editorship of Griffith University's Rob McQueen, and UBC's Wes Pue and with contributions from McQueen, Ian Duncanson, Renisa Mawani, David Williams, Emma Cunliffe, Chidi Oguamanam, W. Wesley Pue, Fatou Camara, and Dianne Kirkby. This paper introduces the volume, forthcoming in late 2007. The central problematique of this issue has previously been explored through the 2005 Law's Empire conference, an informal but vibrant postcolonial legal studies network.

Law's Empire

Taking Rights Seriously.

New democracies around the world have adopted constitutional courts to oversee the operation of democratic politics. Where does judicial power come from, how does it develop in the early stages of democratic liberalization, and what political conditions support its expansion? This book answers these questions through an examination of three constitutional courts in Asia: Taiwan, Korea, and Mongolia. In a region that has traditionally viewed law as a tool of authoritarian rulers, constitutional courts in these three societies are becoming a real constraint on government. In contrast with conventional culturalist accounts, this book argues that the design and functioning of constitutional review are largely a function of politics and interests. Judicial review - the power of judges to rule an act of a legislature or national leader unconstitutional - is a solution to the problem of uncertainty in constitutional design. By providing 'insurance' to prospective electoral losers, judicial review can facilitate democracy.

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Keith E. Whittington

Papers

What Can Professors Say in Public? Extramural Speech and the First Amendment