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This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the funadmental theorem of stable reduction of Deligne-Mumford. The book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are therefore few, and the book should suit a graduate student. It contains many examples and nearly 600 exercises.
And in one celebrated Alaska gold rush case, the court in 1900 thwarted an attempt to steal vast sums of gold by judicial process in Nome, Alaska.
In this book one of Europe's foremost sociologists offers a profound and accessible overview of the trajectory of European societies, East and West, since the end of World War II. Combining theoretical depth with factual analysis, Göran Therborn addresses the questions that underpin an understanding of the nature of European modernity, including: To what extent is the period 1945-2000 producing fundamental change and what are the areas of continuity? Have the societies of Europe become more similar to others on the globe or more distinctively European? What are the prospects of Europe after decades of postwar change and the end of the Cold War? Issues covered include the division of paid and unpaid labour, patterns of rights in different social spheres, the development of mass consumption, the evolution of risks, the spatial range of economic and cultural change, collective memory and identities, the geography of happiness, and modes of collective action. The author relates these issues to the two great social steering projects of the period - socialism in the East and the European Union in the West.
While the coerced human experiments are notorious among all the atrocities under National Socialism, they have been marginalised by mainstream historians. This book seeks to remedy the marginalisation, and to place the experiments in the context of the broad history of National Socialism and the Holocaust. Paul Weindling bases this study on the reconstruction of a victim group through individual victims' life histories, and by weaving the victims' experiences collectively together in terms of different groupings, especially gender, ethnicity and religion, age, and nationality. The timing of the experiments, where they occurred, how many victims there were, and who they were, is analysed, as are hitherto under-researched aspects such as Nazi anatomy and executions. The experiments are also linked, more broadly, to major elements in the dynamic and fluid Nazi power structure and the implementation of racial policies. The approach is informed by social history from below, exploring both the rationales and motives of perpetrators, but assessing these critically in the light of victim narratives.

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