Diophantine Geometry as Galois Theory in the Mathematics of Serge Lang

A remark about the role of Galois theory in Diophantine geometry as reflected in the work of Serge Lang. An entry in `The mathematical contributions of Serge Lang.

Imperfect justice : Fritz Lang's Fury (1936) and cinema's use of the trial form

This essay examines Fritz Lang's portrayal and use of justice in his first Hollywood film, Fury (1936) a film in which the main character, Joe Wilson (played by Spencer Tracy) is mistakenly arrested for a crime he did not commit. Lang was one of many notable German émigrés who fled Nazi Germany for America and eventually Hollywood. He returned on several occasions to the theme of justice, which is my starting point for this article. Before analysing Fury in detail, in particular its final trial scene, the article compares the film briefly to other Lang films about the law such as Beyond a Reasonable Doubt. Lang's conception of justice differs from the dominant Hollywood view of the law, a realisation that is discussed in relation to other depictions of the law in Hollywood (such as Twelve Angry Men, To Kill a Mockingbird). In Lang's cinema, the law is not a fixed, stable and trustworthy institution, but rather one that is gullible and open to abuse. Lang places more faith in notions of personal moral justice, which win out in the end in Fury. This article also contextualises Fury and the work of Fritz Lang within existing discussions of the law and film, from which Lang is largely and notably absent

Manfred Hutter (ed.): Religionsinterne Kritik und religiöser Pluralismus im gegenwärtigen Südostasien: Frankfurt/Main: Peter Lang, 2008, [= Religionswissenschaft 15], ISBN 978-3-631-57500-0, 253 pages [Rezension]

Review of the edited volume: Manfred Hutter (ed.): Religionsinterne Kritik und religiöser Pluralismus im gegenwärtigen Südostasien Frankfurt/Main: Peter Lang, 2008, [= Religionswissenschaft 15], ISBN 978-3-631-57500-0, 253 pagesBuchbesprechung: Manfred Hutter (ed.): Religionsinterne Kritik und religiöser Pluralismus im gegenwärtigen Südostasien. Frankfurt/Main: Peter Lang, 2008, [= Religionswissenschaft 15], ISBN 978-3-631-57500-0, 253 page

Strongly semistable sheaves and the Mordell-Lang conjecture over function fields

We give a new proof of the Mordell-Lang conjecture in positive characteristic, in the situation where the variety under scrutiny is a smooth subvariety of an abelian variety. Our proof is based on the theory of semistable sheaves in positive characteristic, in particular on Langer's theorem that the Harder-Narasimhan filtration of sheaves becomes strongly semistable after a finite number of iterations of Frobenius pull-backs. The interest of this proof is that it provides simple effective bounds (depending on the degree of the canonical line bundle) for the degree of the isotrivial finite cover whose existence is predicted by the Mordell-Lang conjecture. We also present a conjecture on the Harder-Narasimhan filtration of the cotangent bundle of a smooth projective variety of general type in positive characteristic and a conjectural refinement of the Bombieri-Lang conjecture in positive characteristic

Underlying global features of the x-ray light curves of {\it swift} gamma-ray bursts

With its rapid response, {\it Swift} has revealed plenty of unexpected properties of gamma-ray bursts (GRBs). With an abundance of observations, our current understanding is only limited by complexity of early X-ray light curves. In this work, based on the public {\it Swift} data of 150 well-monitored GRBs with measured redshifts, we find some interesting global features in the rest-frame X-ray light curves. The distinct spectral behaviors between the prompt emission and the afterglow emission implies dissimilar radiation scenarios. Interestingly, an unforeseen plateau is exhibited in the prompt X-ray light curves despite the presence of complex spikes, which might indicate the presence of a steady central engine. In particular, the seemingly continuous evolution with a single power law from the prompt to the afterglow of most GRBs might place strong constraints on the theoretical models.Comment: 16 pages, 3 figures, published in ApJ Letter