Bost-Connes-Marcolli systems for Shimura varieties. I. Definitions and formal analytic properties

We construct a quantum statistical mechanical system $(A,s)$ analogous to the systems constructed by Bost-Connes and Connes-Marcolli in the case of Shimura varieties. Along the way, we define a new Bost-Connes system for number fields which has the ``correct'' partition function and the ``correct'' symmetries. We give a formalism that applies to general Shimura data $(G,X)$. The object of this series of papers is to show that these systems exhibit phase transitions with spontaneous symmetry breaking, and to classify their KMS states, at least for low temperature.Comment: 37 pages, LaTe

Nickel hydrogen capacity loss

The results of tests to assess capacity loss in nickel hydrogen cells are presented in outline form. The effects of long storage (greater than 1 month), high hydrogen pressure storage, high cobalt content, and recovery actions are addressed

From Waterloo to Wembley: A Comparison of International Football and International Warfare in Building Nationalism

International football has often been described as a soft way for nations to go to war. This analysis is too simplistic, but the reference to warfare is not uninteresting and provides the starting point for this dissertation. Having noticed the national fervour surrounding international football, and recognised warfare’s nationalist builder power, it seeks to explore the extent to which international football and international war are comparable in building nationalism. It adopts an ethno-symbolist perspective on nations and nationalism, hence seen as modern constructions rooted in more ancient cultures and groups. It argues that international football and international war are, indeed, using the same mechanisms to build nationalism, but that this comparison might evolve with globalisation, and, especially, the associated immigration flows and diasporas. More precisely, the first part of the answer argues that within the traditional framework of the nation-state, myth building, tradition shaping, and rivalry constructions are nationalist elements shared by international war and football. The second part is more hypothetical and seeks to explore how football can be a new nationalism vector for diasporas, linking national groups no longer sharing a unique territory. This dissertation illustrates each point with two case studies: a small set of detailed interviews with Dutch people to analyse the importance of football myths in building their nationalism, and a questionnaire, carried online and in person near Paris, with 46 members of the Portuguese community in France, to understand how the role of football in building nationalism might evolve

A note on the nonlinear derived Cauchy problem

We define and study a generalization of the analytic Cauchy problem, that specializes to the Cauchy-Kowaleskaya-Kashiwara problem in the linear case. The main leitmotive of this text is to adapt Kashiwara's formulation of this problem both to the relatively D-algebraic case and to the derived analytic situation. Along the way, we define the characteristic variety of a derived nonlinear partial differential system

ANALYTIC SPECTRUM OF RIG CATEGORIES

Abstract. We define the analytic spectrum of a rig category (A, ⊕, ⊗), and equip it with a sheaf of categories of rational functions. If the category is additive, we define a sheaf of categories of analytic functions. We relate this construction to Berkovich’s analytic spaces, to Durov’s generalized schemes and to Haran’s F-schemes. We use these relations to define analytic versions of Arakelov compactifications of affine arithmetic varieties. 1