Some Definability Results in Abstract Kummer Theory

Let $S$ be a semiabelian variety over an algebraically closed field, and let $X$ be an irreducible subvariety not contained in a coset of a proper algebraic subgroup of $S$. We show that the number of irreducible components of $[n]^{-1}(X)$ is bounded uniformly in $n$, and moreover that the bound is uniform in families $X_t$. We prove this by purely Galois-theoretic methods. This proof applies in the more general context of divisible abelian groups of finite Morley rank. In this latter context, we deduce a definability result under the assumption of the Definable Multiplicity Property (DMP). We give sufficient conditions for finite Morley rank groups to have the DMP, and hence give examples where our definability result holds.Comment: 21 pages; minor notational fixe

On Variants of CM-triviality

We introduce a generalization of CM-triviality relative to a fixed invariant collection of partial types, in analogy to the Canonical Base Property defined by Pillay, Ziegler and Chatzidakis which generalizes one-basedness. We show that, under this condition, a stable field is internal to the family, and a group of finite Lascar rank has a normal nilpotent subgroup such that the quotient is almost internal to the family

Zilber's notion of logically perfect structure: Universal Covers

We sketch recent interactions between model theory and a roughly 150-year old study of analytic functions involving complex analysis, algebraic topology, and number theory, centered in canonicity of universal covers. Towards this goal we discuss in a systematic and unified way several examples indicating the main ideas of the proofs and the necessary changes in method for different situations: exponential covers, modular and Shimura curves, Shimura and abelian varieties, and coherent families of smooth covers.Comment: 1 figur

PAC structures as invariants of finite group actions

We study model theory of actions of finite groups on substructures of a stable structure. We give an abstract description of existentially closed actions as above in terms of invariants and PAC structures. We show that if the corresponding PAC property is first order, then the theory of such actions has a model companion. Then, we analyze some particular theories of interest (mostly various theories of fields of positive characteristic) and show that in all the cases considered the PAC property is first order

Poverty, possessions and proper living : constructing and contesting propriety in Soweto and Lusaka City

Bibliography: 131-137.Recent material culture theory points out how material possessions are woven into the fabric of lives, shaping social relations and texturing people's meanings and interpretation of their world. This study embarks on exploring aspects of this objected fabric, in the context of urban working black South Africans, living in three different township suburbs in Gauteng, in four differing housing circumstances, in the mid-1990s and in the midst of much uncertainty of what the future might hold for poor urban residents. Drawing on participant observation, ethnographic interviews, and household and appliance ownership surveys, the study explores the ways in which domestic objects- appliances specifically - function symbolically for a set of people living in Soweto formal houses, backyard shacks, an informal settlement and in Lusaka City site-and -service settlement on the West Rand, in Gauteng, South Africa. I examine symbolic constructions and creations in these people's homes, gleaning some of the meaning people attributed to particular modes of equipping their homes, and how aspects of their image of themselves and each other were presented, acted out, created, 'conversationed', contested and negotiated through material goods

Assembling States: Community Formation And The Emergence Of The Inca Empire

This dissertation investigates the processes through which the Inca state emerged in the south-central Andes, ca. 1400 CE in Cusco, Peru, an area that was to become the political center of the largest indigenous empire in the Western hemisphere. Many approaches to this topic over the past several decades have framed state formation in a social evolutionary framework, a perspective that has come under increasing critique in recent years. I argue that theoretical attempts to overcome these problems have been ultimately confounded, and in order to resolve these contradictions, an ontological shift is needed. I adopt a relational perspective towards approaching the emergence of the Inca state – in particular, that of assemblage theory. Treating states and other complex social entities as assemblages means understanding them as open-ended and historically individuated phenomena, emerging from centuries or millennia of sociopolitical, cultural, and material engagements with the human and non-human world, and constituted over the longue durée. This means that understanding the emergence of the Inca state, and the historically contingent form it took, requires investigating the transformations of local and regional communities in the Cusco heartland. The multiscalar nature of this type of investigation also demands an examination of processes occurring at particular local communities through time. To resolve this, I directed excavations at the archaeological site of Minaspata, located in the Lucre Basin in the southeastern part of the Cusco region, followed by analyses of the material remains recovered from the site. These include fine-grained investigations of the ceramic patterns, the faunal and macrobotanical remains, and the procurement of obsidian through long-distance exchange. By comparing these patterns to those of the larger Cusco region, an understanding of how the Cusco regional community cohered and broke apart at various points in time can be gained. This regional community eventually gave rise to the Inca state, providing the raw material for Inca projects of sovereignty and subject-making. Although the period before Inca emergence was marked by processes focused on the localization of community, the sociocultural and material frameworks established through complex histories of interaction over millennia enabled the Cusco region to reproduce itself as a self-recognizing, coherent social entity, a critical necessity for the emergence of Inca sovereignty